Abstract
This chapter describes numerical methods to directly solve the original constrained problem. It also discusses basic concepts, ideas, and definitions of the terms used in numerical methods for constrained optimization. Further the status of a constraint at a design point is defined, along with active, inactive, violated, and ɛ-active constraints. Normalization of constraints, its advantages, ideas of a descent function, and convergence of algorithms are also explained. Just as for unconstrained problems, several methods have been developed and evaluated for the general constrained optimization problems. Most methods follow the two-phase approach as for the unconstrained problems: the search direction and step size determination phases. The approach followed in this chapter is to describe the underlying ideas and concepts of the methods. Conceptually, algorithms for unconstrained and constrained optimization problems are based on the same iterative philosophy. There is one important difference, however: Constraints must be considered while determining the search direction as well as the step size. A different procedure for determining either one can give a different optimization algorithm.
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