ABSTRACT
This chapter is concerned with the problem of determining a solution of a constrained nonlinear programming problem. The approach is to replace a constrained problem with one that is unconstrained. In the first approach, the constrained problem is converted into an unconstrained problem by adding a penalty function,p(x), to the objective function f (x). The solutions, {Xk}, of the sequence will usually approach, in some sense, the solution of the original problem. The process terminates whenever the required accuracy has been obtained, or whenever some solution, xk, is generated that is a feasible solution of the original problem. The difference in the second approach is that the solutions, xk, are all feasible solutions of the original problem. Both of these methods can possess the undesirable property of slow convergence. The chapter explains the penalty function method using Lagrange multipliers to obtain a more efficient method, and the technique is called the method of multipliers.
