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A convex optimization problem is defined by two ingredients:<ref>{{cite book |last1=Hiriart-Urruty |first1=Jean-Baptiste |url=https://books.google.com/books?id=Gdl4Jc3RVjcC&q=lemarechal+convex+analysis+and+minimization |title=Convex analysis and minimization algorithms: Fundamentals |last2=Lemaréchal |first2=Claude |year=1996 |isbn=9783540568506 |page=291}}</ref><ref>{{cite book |last1=Ben-Tal |first1=Aharon |url=https://books.google.com/books?id=M3MqpEJ3jzQC&q=Lectures+on+Modern+Convex+Optimization:+Analysis,+Algorithms, |title=Lectures on modern convex optimization: analysis, algorithms, and engineering applications |last2=Nemirovskiĭ |first2=Arkadiĭ Semenovich |year=2001 |isbn=9780898714913 |pages=335–336}}</ref>
* The ''objective function'', which is a real-valued [[convex function]] of ''n'' variables, <math>f :\mathcal D \subseteq \mathbb{R}^n \to \mathbb{R}</math>
* The ''feasible set'', which is a convex subset <math>C\subseteq \mathbb{R}^n</math>.
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