Convex Optimization

Authored by: Florian Jarre , Stephen A. Vavasis

Algorithms and Theory of Computation Handbook

Print publication date:  November  2009
Online publication date:  November  2009

Print ISBN: 9781584888222
eBook ISBN: 9781584888239
Adobe ISBN:

10.1201/9781584888239-c32

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Abstract

Nonlinear constrained optimization refers to the problem of minimizing f (x) subject to x ∈ D, where D is a subset of R n and f is a continuous function from D to R. Thus, an input instance is a specification of D, called the feasible set, and f, called the objective function. The output from an optimization algorithm is either a point x *D, called an optimizer or global optimizer, such that f (x *) ≤ f (x) for all x ∈ D, or else a statement (preferably accompanied by a certificate) that no such x * exists. The terms minimizer and global minimizer are also used

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