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 : R^{n} → R is convex and twice continuously differentiable, and A ∈ R^{p×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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