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Convex Optimization by Lieven Vandenberghe, Stephen Boyd

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Chapter 4

Convex optimization problems

4.1 Optimization problems

4.1.1  Basic terminology

We use the notation

(4.1)

to describe the problem of finding an x that minimizes f0(x) among all x that satisfy the conditions fi(x)0, i = 1, . . . , m, and hi(x) = 0, i = 1, . . . , p. We call x Rn the optimization variable and the function f0 : Rn R the objective function or cost function. The inequalities fi(x)0 are called inequality constraints, and the corresponding functions fi : Rn R are called the inequality constraint functions. The equations hi(x) = 0 are called the equality constraints, and the functions hi : Rn R are the

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