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power.html
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If expr is a CVXR expression, then expr^p is equivalent to power(expr,p)." />
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<h1>Elementwise Power</h1>
<small class="dont-index">Source: <a href='https://github.com/cvxgrp/CVXR/blob/master/R/expressions.R'><code>R/expressions.R</code></a>, <a href='https://github.com/cvxgrp/CVXR/blob/master/R/exports.R'><code>R/exports.R</code></a></small>
<div class="hidden name"><code>power.Rd</code></div>
</div>
<div class="ref-description">
<p>Raises each element of the input to the power \(p\).
If <code>expr</code> is a CVXR expression, then <code>expr^p</code> is equivalent to <code>power(expr,p)</code>.</p>
</div>
<pre class="usage"># S4 method for Expression,numeric
^(e1, e2)
power(x, p, max_denom = 1024)</pre>
<h2 class="hasAnchor" id="arguments"><a class="anchor" href="#arguments"></a>Arguments</h2>
<table class="ref-arguments">
<colgroup><col class="name" /><col class="desc" /></colgroup>
<tr>
<th>e1</th>
<td><p>An <a href='Expression-class.html'>Expression</a> object to exponentiate.</p></td>
</tr>
<tr>
<th>e2</th>
<td><p>The power of the exponential. Must be a numeric scalar.</p></td>
</tr>
<tr>
<th>x</th>
<td><p>An <a href='Expression-class.html'>Expression</a>, vector, or matrix.</p></td>
</tr>
<tr>
<th>p</th>
<td><p>A scalar value indicating the exponential power.</p></td>
</tr>
<tr>
<th>max_denom</th>
<td><p>The maximum denominator considered in forming a rational approximation of <code>p</code>.</p></td>
</tr>
</table>
<h2 class="hasAnchor" id="details"><a class="anchor" href="#details"></a>Details</h2>
<p>For \(p = 0\) and \(f(x) = 1\), this function is constant and positive.
For \(p = 1\) and \(f(x) = x\), this function is affine, increasing, and the same sign as \(x\).
For \(p = 2,4,8,\ldots\) and \(f(x) = |x|^p\), this function is convex, positive, with signed monotonicity.
For \(p < 0\) and \(f(x) = \)</p><ul>
<li><p>\(x^p\) for \(x > 0\)</p></li>
<li><p>\(+\infty\)\(x \leq 0\)</p></li>
</ul><p>, this function is convex, decreasing, and positive.
For \(0 < p < 1\) and \(f(x) =\)</p><ul>
<li><p>\(x^p\) for \(x \geq 0\)</p></li>
<li><p>\(-\infty\)\(x < 0\)</p></li>
</ul><p>, this function is concave, increasing, and positivea.
For \(p > 1, p \neq 2,4,8,\ldots\) and \(f(x) = \)</p><ul>
<li><p>\(x^p\) for \(x \geq 0\)</p></li>
<li><p>\(+\infty\)\(x < 0\)</p></li>
</ul><p>, this function is convex, increasing, and positive.</p>
<h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2>
<pre class="examples"><div class='input'><span class='kw'>if</span> (<span class='fl'>FALSE</span>) {
<span class='no'>x</span> <span class='kw'><-</span> <span class='fu'><a href='Variable-class.html'>Variable</a></span>()
<span class='no'>prob</span> <span class='kw'><-</span> <span class='fu'><a href='Problem-class.html'>Problem</a></span>(<span class='fu'><a href='Minimize-class.html'>Minimize</a></span>(<span class='fu'>power</span>(<span class='no'>x</span>,<span class='fl'>1.7</span>) + <span class='fu'>power</span>(<span class='no'>x</span>,-<span class='fl'>2.3</span>) - <span class='fu'>power</span>(<span class='no'>x</span>,<span class='fl'>0.45</span>)))
<span class='no'>result</span> <span class='kw'><-</span> <span class='fu'><a href='psolve.html'>solve</a></span>(<span class='no'>prob</span>)
<span class='no'>result</span>$<span class='no'>value</span>
<span class='no'>result</span>$<span class='fu'>getValue</span>(<span class='no'>x</span>)
}</div></pre>
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