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:

equation

subject to

(7.1) equation

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 ...

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