# Convex optimization

## Subfield of mathematical optimization / From Wikipedia, the free encyclopedia

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**Convex optimization** is a subfield of mathematical optimization that studies the problem of minimizing convex functions over convex sets (or, equivalently, maximizing concave functions over convex sets). Many classes of convex optimization problems admit polynomial-time algorithms,^{[1]} whereas mathematical optimization is in general NP-hard.^{[2]}^{[3]}^{[4]}