Convex Optimization Task

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A Convex Optimization Task is an optimization task that accepts a convex function (over convex sets).



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  • http://en.wikipedia.org/wiki/Convex_optimization
    • Convex optimization, a subfield of mathematical optimization, studies the problem of minimizing convex functions over convex sets. Given a real vector space [math]\displaystyle{ X }[/math] together with a convex, real-valued function [math]\displaystyle{ f:\mathcal{X}\to \mathbb{R} }[/math] defined on a convex subset [math]\displaystyle{ \mathcal{X} }[/math] of [math]\displaystyle{ X }[/math], the problem is to find a point [math]\displaystyle{ x^* }[/math] in [math]\displaystyle{ \mathcal{X} }[/math] for which the number [math]\displaystyle{ f(x) }[/math] is smallest, i.e., a point [math]\displaystyle{ x^* }[/math] such that [math]\displaystyle{ f(x^*) \le f(x) }[/math] for all [math]\displaystyle{ x \in \mathcal{X} }[/math].

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