This chapter deals with techniques that are applicable to the solution of the constrained optimization problem:
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|
|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|
|Rosen's gradient projection method ...|