Engineering Optimization, 5th Edition

7 Nonlinear Programming III: Constrained Optimization Techniques

7.1 Introduction

This chapter deals with techniques that are applicable to the solution of the constrained optimization problem:

subject to

(7.1)

There are many techniques available for the solution of a constrained nonlinear programming problem. All the methods can be classified into two broad categories: direct methods and indirect methods, as shown in Table 7.1. In the direct methods, the constraints are handled in an explicit manner, whereas in most of the indirect methods, the constrained problem is solved as a sequence of unconstrained minimization problems. We discuss in this chapter all the methods indicated in Table 7.1.

Table 7.1 Constrained Optimization Techniques.

Direct methods	Indirect methods
Random search methods	Transformation of variables technique
Heuristic search methods	Sequential unconstrained minimization techniques
Complex method
Objective and constraint approximation methods	Interior penalty function method
Exterior penalty function method
Sequential linear programming method	Augmented Lagrange multiplier method
Sequential quadratic programming method
Methods of feasible directions
Zoutendijk's method
Rosen's gradient projection method ...