Optimization Problems Subject to Continuous Inequality Constraints

In this chapter, we shall present two computational approaches to solve a general class of optimization problems subject to continuous inequality constraints. The first approach is known as the constraint transcription method, while the other approach is referred to as an exact penalty function method. To begin, we first consider the problem of finding a feasible solution to a system of nonlinear inequality constraints. Using the constrained transcription method with a local smoothing technique, the problem is approximated by an unconstrained optimization problem. This approach is extended to find a feasible solution of a system of continuous inequality constraints. We then move on to consider the optimization problems subject to continuous inequality constraints. The constraint transcription method is used in conjunction with a local smoothing method to develop two computational methods to solve this general optimization problem with continuous inequality constraints. We then move on to introduce the second approach (i.e., the exact penalty function approach) to solving the same class of continuous inequality constrained optimization problems.