Content deleted Content added
Erel Segal (talk | contribs) No edit summary |
Erel Segal (talk | contribs) |
||
Line 40:
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>
===
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}}
| |||