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Many optimization problems can be equivalently formulated in this standard form. For example, the problem of maximizing a [[concave function]] <math>f</math> can be re-formulated equivalently as the problem of minimizing the convex function <math>-f</math>. The problem of maximizing a concave function over a convex set is commonly called a convex optimization problem.<ref>{{cite web | url=https://www.solver.com/convex-optimization | title=Optimization Problem Types - Convex Optimization | date=9 January 2011 }}</ref>
===Standard form with linear objective{{Anchor|linear}}===
In the standard form it is possible to assume, without loss of generality, that the objective function ''f'' is a [[linear function]]. This is because any program with a general objective can be transformed into a program with a linear objective by adding a single variable t and a single constraint, as follows::<ref name=":02">{{Cite book |last=Arkadi Nemirovsky |url=https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=8c3cb6395a35cb504019f87f447d65cb6cf1cdf0 |title=Interior point polynomial-time methods in convex programming |year=2004}}</ref>{{Rp|___location=1.4}}
:<math>\begin{align}
&\underset{\mathbf{x},t}{\operatorname{minimize}}& & t \\
&\operatorname{subject\ to}
& &f(\mathbf{x}) - t \leq 0 \\
&& &g_i(\mathbf{x}) \leq 0, \quad i = 1, \dots, m \\
&&&h_i(\mathbf{x}) = 0, \quad i = 1, \dots, p,
\end{align}</math>
==Properties==
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