Constrained optimization algorithms - Mines Nancy

We again consider the general, possibly nonconvex optimization problem

\begin{array}{lll} \text{minimize} & f_0(x) & \\ \text{subject to} & x\in \Omega \end{array}

(1)

where the constraint set $\Omega$ is parameterized by equality and inequality constraints

\Omega = \left\lbrace x \in \mathbb{R}^n \mid f_i(x) \leq 0, \: i = 1, \ldots, m, \quad h_i(x) = 0, \: i = 1, \ldots,p\right\rbrace

(2)

For simplicity, we assume in this section that the domain $\mathcal{D}= \mathbb{R}^n$ , hence constraint set and feasible set coincide $\Omega = \mathcal{F}$ .

In this chapter, we introduce several algorithmic strategies to solve such optimization problem.

8 Constrained optimization algorithms