# Nonlinear Programming

• Osman Güler
Chapter
Part of the Graduate Texts in Mathematics book series (GTM, volume 258)

## Abstract

A nonlinear program, or a mathematical program, is a constrained optimization (say minimization) problem having the form min
$$\begin{array}{ll} \min & f(x)\\ {\rm{s.t.}} & g_i(x) \leq 0, \quad i = 1, \ldots, r, \quad (P)\\ {} & h_j(x) = 0, \quad j = 1,\ldots,m,\\ \end{array}$$
(9.1)
where f, $$f, \{g_i\}^{r}_{1}$$, and $$\{h_j\}^m_1$$are real-valued functions defined on some subsets of Rn. The function f is called the objective function of (P), and the inequalities and equalities involving g i and h j , respectively, are called the constraints of the problem. The feasible region (or constraint set) of (P) is the set of all points satisfying all the constraints,
$$\mathcal{F}(P) = \{x \in \mathbb{R}^n\ :\ g_i(x) \leq 0, i = 1.,\ldots, r, h_j(x) = 0, j = 1, \ldots,m\}.$$

## Keywords

Nonlinear Programming Feasible Region Nonlinear Program Feasible Point Active Constraint
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.