mirror of
https://github.com/boostorg/math.git
synced 2026-02-25 04:22:15 +00:00
334 lines
34 KiB
HTML
334 lines
34 KiB
HTML
<html>
|
|
<head>
|
|
<meta charset="UTF-8">
|
|
<title>minimize</title>
|
|
<link rel="stylesheet" href="../../math.css" type="text/css">
|
|
<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot">
|
|
<link rel="home" href="../../index.html" title="Math Toolkit 4.2.1">
|
|
<link rel="up" href="../gd_opt.html" title="Gradient Based Optimizers">
|
|
<link rel="prev" href="lbfgs.html" title="L-BFGS">
|
|
<link rel="next" href="policies.html" title="Reverse Mode autodiff policies">
|
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
|
</head>
|
|
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
|
|
<table cellpadding="2" width="100%"><tr>
|
|
<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td>
|
|
<td align="center"><a href="../../../../../../index.html">Home</a></td>
|
|
<td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td>
|
|
<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td>
|
|
<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td>
|
|
<td align="center"><a href="../../../../../../more/index.htm">More</a></td>
|
|
</tr></table>
|
|
<hr>
|
|
<div class="spirit-nav">
|
|
<a accesskey="p" href="lbfgs.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../gd_opt.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="policies.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
|
|
</div>
|
|
<div class="section">
|
|
<div class="titlepage"><div><div><h3 class="title">
|
|
<a name="math_toolkit.gd_opt.minimize"></a><a class="link" href="minimize.html" title="minimize">minimize</a>
|
|
</h3></div></div></div>
|
|
<h5>
|
|
<a name="math_toolkit.gd_opt.minimize.h0"></a>
|
|
<span class="phrase"><a name="math_toolkit.gd_opt.minimize.synopsis"></a></span><a class="link" href="minimize.html#math_toolkit.gd_opt.minimize.synopsis">Synopsis</a>
|
|
</h5>
|
|
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">optimization</span><span class="special">/</span><span class="identifier">minimizer</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span>
|
|
|
|
<span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span>
|
|
<span class="keyword">namespace</span> <span class="identifier">math</span> <span class="special">{</span>
|
|
<span class="keyword">namespace</span> <span class="identifier">optimization</span> <span class="special">{</span>
|
|
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">RealType</span><span class="special">></span>
|
|
<span class="keyword">struct</span> <span class="identifier">optimization_result</span>
|
|
<span class="special">{</span>
|
|
<span class="identifier">size_t</span> <span class="identifier">num_iter</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span>
|
|
<span class="identifier">RealType</span> <span class="identifier">objective_value</span><span class="special">;</span>
|
|
<span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special"><</span><span class="identifier">RealType</span><span class="special">></span> <span class="identifier">objective_history</span><span class="special">;</span>
|
|
<span class="keyword">bool</span> <span class="identifier">converged</span><span class="special">;</span>
|
|
<span class="special">};</span>
|
|
|
|
<span class="comment">/* Minimize an objective using a given optimizer.
|
|
*
|
|
* The optimizer `opt` must expose a `step()` method and the associated
|
|
* typedefs:
|
|
* - argument_container_t
|
|
* - real_type_t
|
|
*
|
|
* The behavior of the minimization loop is controlled by policy objects:
|
|
* - ConstraintPolicy: projects variables onto a feasible set
|
|
* - ConvergencePolicy: determines when convergence has been reached
|
|
* - TerminationPolicy: determines when optimization must stop regardless
|
|
* of convergence (e.g. max iterations)
|
|
*
|
|
* The function returns an `optimization_result` summarizing the run.
|
|
*/</span>
|
|
<span class="keyword">template</span><span class="special"><</span><span class="keyword">class</span> <span class="identifier">Optimizer</span><span class="special">,</span>
|
|
<span class="keyword">class</span> <span class="identifier">ConstraintPolicy</span> <span class="special">=</span>
|
|
<span class="identifier">unconstrained_policy</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">Optimizer</span><span class="special">::</span><span class="identifier">argument_container_t</span><span class="special">>,</span>
|
|
<span class="keyword">class</span> <span class="identifier">ConvergencePolicy</span> <span class="special">=</span>
|
|
<span class="identifier">gradient_norm_convergence_policy</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">Optimizer</span><span class="special">::</span><span class="identifier">real_type_t</span><span class="special">>,</span>
|
|
<span class="keyword">class</span> <span class="identifier">TerminationPolicy</span> <span class="special">=</span> <span class="identifier">max_iter_termination_policy</span><span class="special">></span>
|
|
<span class="keyword">auto</span> <span class="identifier">minimize</span><span class="special">(</span><span class="identifier">Optimizer</span><span class="special">&</span> <span class="identifier">opt</span><span class="special">,</span>
|
|
<span class="identifier">ConstraintPolicy</span> <span class="identifier">project</span> <span class="special">=</span> <span class="identifier">ConstraintPolicy</span><span class="special">{},</span>
|
|
<span class="identifier">ConvergencePolicy</span> <span class="identifier">converged</span> <span class="special">=</span>
|
|
<span class="identifier">ConvergencePolicy</span><span class="special">{</span>
|
|
<span class="keyword">static_cast</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">Optimizer</span><span class="special">::</span><span class="identifier">real_type_t</span><span class="special">>(</span><span class="number">1e-3</span><span class="special">)</span> <span class="special">},</span>
|
|
<span class="identifier">TerminationPolicy</span> <span class="identifier">terminate</span> <span class="special">=</span> <span class="identifier">TerminationPolicy</span><span class="special">(</span><span class="number">100000</span><span class="special">),</span>
|
|
<span class="keyword">bool</span> <span class="identifier">history</span> <span class="special">=</span> <span class="keyword">true</span><span class="special">)</span>
|
|
</pre>
|
|
<p>
|
|
This header provides a generic driver function <code class="computeroutput"><span class="identifier">minimize</span></code>
|
|
that repeatedly advances an optimizer via <code class="computeroutput"><span class="identifier">step</span><span class="special">()</span></code>, optionally projects parameters onto a
|
|
constraint set, and stops when either a convergence criterion is met or a
|
|
termination criterion triggers.
|
|
</p>
|
|
<h5>
|
|
<a name="math_toolkit.gd_opt.minimize.h1"></a>
|
|
<span class="phrase"><a name="math_toolkit.gd_opt.minimize.parameters"></a></span><a class="link" href="minimize.html#math_toolkit.gd_opt.minimize.parameters">Parameters</a>
|
|
</h5>
|
|
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
|
|
<li class="listitem">
|
|
<code class="computeroutput"><span class="identifier">Optimizer</span><span class="special">&</span>
|
|
<span class="identifier">opt</span></code> : Optimizer instance.
|
|
</li>
|
|
<li class="listitem">
|
|
<code class="computeroutput"><span class="identifier">ConstraintPolicy</span> <span class="identifier">project</span></code>
|
|
: Projection policy applied after each <code class="computeroutput"><span class="identifier">step</span><span class="special">()</span></code>. Default is <code class="computeroutput"><span class="identifier">unconstrained_policy</span></code>
|
|
(no projection).
|
|
</li>
|
|
<li class="listitem">
|
|
<code class="computeroutput"><span class="identifier">ConvergencePolicy</span> <span class="identifier">converged</span></code>
|
|
: Stopping criterion. Default is <code class="computeroutput"><span class="identifier">gradient_norm_convergence_policy</span><span class="special">(</span><span class="identifier">tol</span><span class="special">=</span><span class="number">1e-3</span><span class="special">)</span></code>.
|
|
</li>
|
|
<li class="listitem">
|
|
<code class="computeroutput"><span class="identifier">TerminationPolicy</span> <span class="identifier">terminate</span></code>
|
|
: Hard stop criterion. Default is <code class="computeroutput"><span class="identifier">max_iter_termination_policy</span><span class="special">(</span><span class="number">100000</span><span class="special">)</span></code>.
|
|
</li>
|
|
<li class="listitem">
|
|
<code class="computeroutput"><span class="keyword">bool</span> <span class="identifier">history</span></code>
|
|
: If true, records <code class="computeroutput"><span class="identifier">opt</span><span class="special">.</span><span class="identifier">objective_value</span><span class="special">()</span></code> after each iteration in <code class="computeroutput"><span class="identifier">optimization_result</span><span class="special">::</span><span class="identifier">objective_history</span><span class="special">.</span></code>
|
|
</li>
|
|
</ul></div>
|
|
<h5>
|
|
<a name="math_toolkit.gd_opt.minimize.h2"></a>
|
|
<span class="phrase"><a name="math_toolkit.gd_opt.minimize.convergence_policies"></a></span><a class="link" href="minimize.html#math_toolkit.gd_opt.minimize.convergence_policies">Convergence
|
|
Policies</a>
|
|
</h5>
|
|
<p>
|
|
Convergence policies decide when the optimization has converged. Each policy
|
|
has the signature:
|
|
</p>
|
|
<pre class="programlisting"><span class="keyword">bool</span> <span class="keyword">operator</span><span class="special">()(</span><span class="keyword">const</span> <span class="identifier">GradientContainer</span><span class="special">&</span> <span class="identifier">g</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">objective_value</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span>
|
|
</pre>
|
|
<h5>
|
|
<a name="math_toolkit.gd_opt.minimize.h3"></a>
|
|
<span class="phrase"><a name="math_toolkit.gd_opt.minimize.gradient_norm_convergence_policy"></a></span><a class="link" href="minimize.html#math_toolkit.gd_opt.minimize.gradient_norm_convergence_policy">gradient_norm_convergence_policy</a>
|
|
</h5>
|
|
<p>
|
|
Stops when the Euclidean norm of the gradient falls below a tolerance:
|
|
</p>
|
|
<pre class="programlisting"><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">RealType</span><span class="special">></span>
|
|
<span class="keyword">struct</span> <span class="identifier">gradient_norm_convergence_policy</span>
|
|
<span class="special">{</span>
|
|
<span class="keyword">explicit</span> <span class="identifier">gradient_norm_convergence_policy</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">tol</span><span class="special">);</span>
|
|
|
|
<span class="keyword">template</span><span class="special"><</span><span class="keyword">class</span> <span class="identifier">GradientContainer</span><span class="special">></span>
|
|
<span class="keyword">bool</span> <span class="keyword">operator</span><span class="special">()(</span><span class="keyword">const</span> <span class="identifier">GradientContainer</span><span class="special">&</span> <span class="identifier">g</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">objective_v</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span>
|
|
<span class="special">};</span>
|
|
</pre>
|
|
<h5>
|
|
<a name="math_toolkit.gd_opt.minimize.h4"></a>
|
|
<span class="phrase"><a name="math_toolkit.gd_opt.minimize.objective_tol_convergence_policy"></a></span><a class="link" href="minimize.html#math_toolkit.gd_opt.minimize.objective_tol_convergence_policy">objective_tol_convergence_policy</a>
|
|
</h5>
|
|
<p>
|
|
Stops when the absolute change in objective value between successive iterations
|
|
drops below a tolerance:
|
|
</p>
|
|
<pre class="programlisting"><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">RealType</span><span class="special">></span>
|
|
<span class="keyword">struct</span> <span class="identifier">objective_tol_convergence_policy</span>
|
|
<span class="special">{</span>
|
|
<span class="keyword">explicit</span> <span class="identifier">objective_tol_convergence_policy</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">tol</span><span class="special">);</span>
|
|
|
|
<span class="keyword">template</span><span class="special"><</span><span class="keyword">class</span> <span class="identifier">GradientContainer</span><span class="special">></span>
|
|
<span class="keyword">bool</span> <span class="keyword">operator</span><span class="special">()(</span><span class="keyword">const</span> <span class="identifier">GradientContainer</span><span class="special">&,</span> <span class="identifier">RealType</span> <span class="identifier">objective_v</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span>
|
|
<span class="special">};</span>
|
|
</pre>
|
|
<p>
|
|
The first call always returns false
|
|
</p>
|
|
<h5>
|
|
<a name="math_toolkit.gd_opt.minimize.h5"></a>
|
|
<span class="phrase"><a name="math_toolkit.gd_opt.minimize.relative_objective_tol_policy"></a></span><a class="link" href="minimize.html#math_toolkit.gd_opt.minimize.relative_objective_tol_policy">relative_objective_tol_policy</a>
|
|
</h5>
|
|
<p>
|
|
Stops when the relative objective change drops below a tolerance:
|
|
</p>
|
|
<pre class="programlisting"><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">RealType</span><span class="special">></span>
|
|
<span class="keyword">struct</span> <span class="identifier">relative_objective_tol_policy</span>
|
|
<span class="special">{</span>
|
|
<span class="keyword">explicit</span> <span class="identifier">relative_objective_tol_policy</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">rel_tol</span><span class="special">);</span>
|
|
|
|
<span class="keyword">template</span><span class="special"><</span><span class="keyword">class</span> <span class="identifier">GradientContainer</span><span class="special">></span>
|
|
<span class="keyword">bool</span> <span class="keyword">operator</span><span class="special">()(</span><span class="keyword">const</span> <span class="identifier">GradientContainer</span><span class="special">&,</span> <span class="identifier">RealType</span> <span class="identifier">objective_v</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span>
|
|
<span class="special">};</span>
|
|
</pre>
|
|
<p>
|
|
The relative change is computed as:
|
|
</p>
|
|
<pre class="programlisting"><span class="identifier">abs</span><span class="special">(</span><span class="identifier">obj</span> <span class="special">-</span> <span class="identifier">last_obj</span><span class="special">)</span> <span class="special">/</span> <span class="identifier">max</span><span class="special">(</span><span class="number">1</span><span class="special">,</span> <span class="identifier">abs</span><span class="special">(</span><span class="identifier">last_obj</span><span class="special">))</span>
|
|
</pre>
|
|
<h5>
|
|
<a name="math_toolkit.gd_opt.minimize.h6"></a>
|
|
<span class="phrase"><a name="math_toolkit.gd_opt.minimize.combined_convergence_policy"></a></span><a class="link" href="minimize.html#math_toolkit.gd_opt.minimize.combined_convergence_policy">combined_convergence_policy</a>
|
|
</h5>
|
|
<p>
|
|
Combines two convergence policies and stops when either triggers:
|
|
</p>
|
|
<pre class="programlisting"><span class="keyword">template</span><span class="special"><</span><span class="keyword">class</span> <span class="identifier">Policy1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Policy2</span><span class="special">></span>
|
|
<span class="keyword">struct</span> <span class="identifier">combined_convergence_policy</span>
|
|
<span class="special">{</span>
|
|
<span class="identifier">combined_convergence_policy</span><span class="special">(</span><span class="identifier">Policy1</span> <span class="identifier">p1</span><span class="special">,</span> <span class="identifier">Policy2</span> <span class="identifier">p2</span><span class="special">);</span>
|
|
|
|
<span class="keyword">template</span><span class="special"><</span><span class="keyword">class</span> <span class="identifier">GradientContainer</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">></span>
|
|
<span class="keyword">bool</span> <span class="keyword">operator</span><span class="special">()(</span><span class="keyword">const</span> <span class="identifier">GradientContainer</span><span class="special">&</span> <span class="identifier">g</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">obj</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span>
|
|
<span class="special">};</span>
|
|
</pre>
|
|
<h5>
|
|
<a name="math_toolkit.gd_opt.minimize.h7"></a>
|
|
<span class="phrase"><a name="math_toolkit.gd_opt.minimize.termination_policies"></a></span><a class="link" href="minimize.html#math_toolkit.gd_opt.minimize.termination_policies">Termination
|
|
Policies</a>
|
|
</h5>
|
|
<p>
|
|
Termination policies provide a hard stop independent of convergence. Each
|
|
policy has the signature:
|
|
</p>
|
|
<pre class="programlisting"><span class="keyword">bool</span> <span class="keyword">operator</span><span class="special">()(</span><span class="identifier">size_t</span> <span class="identifier">iter</span><span class="special">);</span>
|
|
</pre>
|
|
<h5>
|
|
<a name="math_toolkit.gd_opt.minimize.h8"></a>
|
|
<span class="phrase"><a name="math_toolkit.gd_opt.minimize.max_iter_termination_policy"></a></span><a class="link" href="minimize.html#math_toolkit.gd_opt.minimize.max_iter_termination_policy">max_iter_termination_policy</a>
|
|
</h5>
|
|
<p>
|
|
Stops after a fixed number of iterations
|
|
</p>
|
|
<pre class="programlisting"><span class="keyword">struct</span> <span class="identifier">max_iter_termination_policy</span> <span class="special">{</span> <span class="keyword">explicit</span> <span class="identifier">max_iter_termination_policy</span><span class="special">(</span><span class="identifier">size_t</span> <span class="identifier">max_iter</span><span class="special">);</span> <span class="keyword">bool</span> <span class="keyword">operator</span><span class="special">()(</span><span class="identifier">size_t</span> <span class="identifier">iter</span><span class="special">);</span> <span class="special">};</span>
|
|
</pre>
|
|
<h5>
|
|
<a name="math_toolkit.gd_opt.minimize.h9"></a>
|
|
<span class="phrase"><a name="math_toolkit.gd_opt.minimize.wallclock_termination_policy"></a></span><a class="link" href="minimize.html#math_toolkit.gd_opt.minimize.wallclock_termination_policy">wallclock_termination_policy</a>
|
|
</h5>
|
|
<p>
|
|
Stops after a wall-clock time budget:
|
|
</p>
|
|
<pre class="programlisting"><span class="keyword">struct</span> <span class="identifier">wallclock_termination_policy</span> <span class="special">{</span> <span class="keyword">explicit</span> <span class="identifier">wallclock_termination_policy</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">chrono</span><span class="special">::</span><span class="identifier">milliseconds</span> <span class="identifier">max_time</span><span class="special">);</span> <span class="keyword">bool</span> <span class="keyword">operator</span><span class="special">()(</span><span class="identifier">size_t</span> <span class="identifier">iter</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span> <span class="special">};</span>
|
|
</pre>
|
|
<h5>
|
|
<a name="math_toolkit.gd_opt.minimize.h10"></a>
|
|
<span class="phrase"><a name="math_toolkit.gd_opt.minimize.constraint_and_projection_polici"></a></span><a class="link" href="minimize.html#math_toolkit.gd_opt.minimize.constraint_and_projection_polici">Constraint
|
|
and Projection Policies</a>
|
|
</h5>
|
|
<p>
|
|
Projection policies modify the optimizer variables after each step. Each
|
|
policy has the signature:
|
|
</p>
|
|
<pre class="programlisting"><span class="keyword">void</span> <span class="keyword">operator</span><span class="special">()(</span><span class="identifier">ArgumentContainer</span><span class="special">&</span> <span class="identifier">x</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span>
|
|
</pre>
|
|
<h5>
|
|
<a name="math_toolkit.gd_opt.minimize.h11"></a>
|
|
<span class="phrase"><a name="math_toolkit.gd_opt.minimize.unconstrained_policy"></a></span><a class="link" href="minimize.html#math_toolkit.gd_opt.minimize.unconstrained_policy">unconstrained_policy</a>
|
|
</h5>
|
|
<p>
|
|
No projection; leaves parameters unchanged
|
|
</p>
|
|
<pre class="programlisting"><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">ArgumentContainer</span><span class="special">></span> <span class="keyword">struct</span> <span class="identifier">unconstrained_policy</span> <span class="special">{</span> <span class="keyword">void</span> <span class="keyword">operator</span><span class="special">()(</span><span class="identifier">ArgumentContainer</span><span class="special">&);</span> <span class="special">};</span>
|
|
</pre>
|
|
<h5>
|
|
<a name="math_toolkit.gd_opt.minimize.h12"></a>
|
|
<span class="phrase"><a name="math_toolkit.gd_opt.minimize.box_constraints"></a></span><a class="link" href="minimize.html#math_toolkit.gd_opt.minimize.box_constraints">box_constraints</a>
|
|
</h5>
|
|
<p>
|
|
Clamps each variable into <code class="computeroutput"><span class="special">[</span><span class="identifier">min</span><span class="special">,</span> <span class="identifier">max</span><span class="special">]</span></code>
|
|
</p>
|
|
<pre class="programlisting"><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">ArgumentContainer</span><span class="special">,</span> <span class="keyword">typename</span> <span class="identifier">RealType</span><span class="special">></span> <span class="keyword">struct</span> <span class="identifier">box_constraints</span> <span class="special">{</span> <span class="identifier">box_constraints</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">min</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">max</span><span class="special">);</span> <span class="keyword">void</span> <span class="keyword">operator</span><span class="special">()(</span><span class="identifier">ArgumentContainer</span><span class="special">&</span> <span class="identifier">x</span><span class="special">);</span> <span class="special">};</span>
|
|
</pre>
|
|
<h5>
|
|
<a name="math_toolkit.gd_opt.minimize.h13"></a>
|
|
<span class="phrase"><a name="math_toolkit.gd_opt.minimize.nonnegativity_constraint"></a></span><a class="link" href="minimize.html#math_toolkit.gd_opt.minimize.nonnegativity_constraint">nonnegativity_constraint</a>
|
|
</h5>
|
|
<p>
|
|
Sets anything less than <code class="computeroutput"><span class="number">0</span></code> to
|
|
<code class="computeroutput"><span class="number">0</span></code>
|
|
</p>
|
|
<pre class="programlisting"><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">ArgumentContainer</span><span class="special">,</span> <span class="keyword">typename</span> <span class="identifier">RealType</span><span class="special">></span> <span class="keyword">struct</span> <span class="identifier">nonnegativity_constraint</span> <span class="special">{</span> <span class="keyword">void</span> <span class="keyword">operator</span><span class="special">()(</span><span class="identifier">ArgumentContainer</span><span class="special">&</span> <span class="identifier">x</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span> <span class="special">};</span>
|
|
</pre>
|
|
<h5>
|
|
<a name="math_toolkit.gd_opt.minimize.h14"></a>
|
|
<span class="phrase"><a name="math_toolkit.gd_opt.minimize.l2_ball_constraint"></a></span><a class="link" href="minimize.html#math_toolkit.gd_opt.minimize.l2_ball_constraint">l2_ball_constraint</a>
|
|
</h5>
|
|
<p>
|
|
Projects onto the <code class="computeroutput"><span class="identifier">L2</span></code> ball
|
|
of radius <code class="computeroutput"><span class="identifier">radius</span></code> by uniform
|
|
scaling when needed
|
|
</p>
|
|
<pre class="programlisting"><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">ArgumentContainer</span><span class="special">,</span> <span class="keyword">typename</span> <span class="identifier">RealType</span><span class="special">></span> <span class="keyword">struct</span> <span class="identifier">l2_ball_constraint</span> <span class="special">{</span> <span class="keyword">explicit</span> <span class="identifier">l2_ball_constraint</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">radius</span><span class="special">);</span> <span class="keyword">void</span> <span class="keyword">operator</span><span class="special">()(</span><span class="identifier">ArgumentContainer</span><span class="special">&</span> <span class="identifier">x</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span> <span class="special">};</span>
|
|
</pre>
|
|
<h5>
|
|
<a name="math_toolkit.gd_opt.minimize.h15"></a>
|
|
<span class="phrase"><a name="math_toolkit.gd_opt.minimize.l1_ball_constraint"></a></span><a class="link" href="minimize.html#math_toolkit.gd_opt.minimize.l1_ball_constraint">l1_ball_constraint</a>
|
|
</h5>
|
|
<p>
|
|
Projects onto the <code class="computeroutput"><span class="identifier">L1</span></code> ball
|
|
of radius <code class="computeroutput"><span class="identifier">radius</span></code> by uniform
|
|
scaling
|
|
</p>
|
|
<pre class="programlisting"><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">ArgumentContainer</span><span class="special">,</span> <span class="keyword">typename</span> <span class="identifier">RealType</span><span class="special">></span> <span class="keyword">struct</span> <span class="identifier">l1_ball_constraint</span> <span class="special">{</span> <span class="keyword">explicit</span> <span class="identifier">l1_ball_constraint</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">radius</span><span class="special">);</span> <span class="keyword">void</span> <span class="keyword">operator</span><span class="special">()(</span><span class="identifier">ArgumentContainer</span><span class="special">&</span> <span class="identifier">x</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span> <span class="special">};</span>
|
|
</pre>
|
|
<p>
|
|
This is not the exact Euclidean projection onto the L1 ball; it is a simple
|
|
scaling-based constraint
|
|
</p>
|
|
<h5>
|
|
<a name="math_toolkit.gd_opt.minimize.h16"></a>
|
|
<span class="phrase"><a name="math_toolkit.gd_opt.minimize.simplex_constraint"></a></span><a class="link" href="minimize.html#math_toolkit.gd_opt.minimize.simplex_constraint">simplex_constraint</a>
|
|
</h5>
|
|
<p>
|
|
Projects onto the scaled probability simplex by clipping negatives to <code class="computeroutput"><span class="number">0</span></code> and renormalizing to sum to <code class="computeroutput"><span class="number">1</span></code>
|
|
</p>
|
|
<pre class="programlisting"><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">ArgumentContainer</span><span class="special">,</span> <span class="keyword">typename</span> <span class="identifier">RealType</span><span class="special">></span> <span class="keyword">struct</span> <span class="identifier">simplex_constraint</span> <span class="special">{</span> <span class="keyword">void</span> <span class="keyword">operator</span><span class="special">()(</span><span class="identifier">ArgumentContainer</span><span class="special">&</span> <span class="identifier">x</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span> <span class="special">};</span>
|
|
</pre>
|
|
<h5>
|
|
<a name="math_toolkit.gd_opt.minimize.h17"></a>
|
|
<span class="phrase"><a name="math_toolkit.gd_opt.minimize.function_constraint"></a></span><a class="link" href="minimize.html#math_toolkit.gd_opt.minimize.function_constraint">function_constraint</a>
|
|
</h5>
|
|
<p>
|
|
Wraps a user-provided projection function
|
|
</p>
|
|
<pre class="programlisting"><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">ArgumentContainer</span><span class="special">></span> <span class="keyword">struct</span> <span class="identifier">function_constraint</span> <span class="special">{</span> <span class="keyword">using</span> <span class="identifier">func_t</span> <span class="special">=</span> <span class="keyword">void</span> <span class="special">(*)(</span><span class="identifier">ArgumentContainer</span><span class="special">&);</span> <span class="keyword">explicit</span> <span class="identifier">function_constraint</span><span class="special">(</span><span class="identifier">func_t</span> <span class="identifier">f</span><span class="special">);</span> <span class="keyword">void</span> <span class="keyword">operator</span><span class="special">()(</span><span class="identifier">ArgumentContainer</span><span class="special">&</span> <span class="identifier">x</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span> <span class="special">};</span>
|
|
</pre>
|
|
<h5>
|
|
<a name="math_toolkit.gd_opt.minimize.h18"></a>
|
|
<span class="phrase"><a name="math_toolkit.gd_opt.minimize.unit_sphere_constraint"></a></span><a class="link" href="minimize.html#math_toolkit.gd_opt.minimize.unit_sphere_constraint">unit_sphere_constraint</a>
|
|
</h5>
|
|
<p>
|
|
Normalizes the vector to unit L2 norm
|
|
</p>
|
|
<pre class="programlisting"><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">ArgumentContainer</span><span class="special">,</span> <span class="keyword">typename</span> <span class="identifier">RealType</span><span class="special">></span> <span class="keyword">struct</span> <span class="identifier">unit_sphere_constraint</span> <span class="special">{</span> <span class="keyword">void</span> <span class="keyword">operator</span><span class="special">()(</span><span class="identifier">ArgumentContainer</span><span class="special">&</span> <span class="identifier">x</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span> <span class="special">};</span>
|
|
</pre>
|
|
<p>
|
|
This projects onto the unit sphere (if ||x||_2 > 0)
|
|
</p>
|
|
</div>
|
|
<div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
|
|
Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
|
|
Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
|
|
Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
|
|
Walker, Xiaogang Zhang, and Maksym Zhelyeznyakov<p>
|
|
Distributed under the Boost Software License, Version 1.0. (See accompanying
|
|
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
|
|
</p>
|
|
</div>
|
|
<hr>
|
|
<div class="spirit-nav">
|
|
<a accesskey="p" href="lbfgs.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../gd_opt.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="policies.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
|
|
</div>
|
|
</body>
|
|
</html>
|