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Convex Optimization by Lieven Vandenberghe, Stephen Boyd

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Chapter 10

Equality constrained minimization

10.1  Equality constrained minimization problems

In this chapter we describe methods for solving a convex optimization problem with equality constraints,

(10.1)

where f : Rn R is convex and twice continuously differentiable, and A Rp×n with rank A = p n. The assumptions on A mean that there are fewer equality constraints than variables, and that the equality constraints are independent. We will assume that an optimal solution x exists, and use p to denote the optimal value, p = inf{f(x) |

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