Optimization Methods

Abstract

Optimization is concerned with identifying the best element in a set of competing possibilities. Except in special circumstances, one must use numerical methods to search for solutions iteratively. If one's problem is well‐behaved, for example, the objective to be minimized is smooth and the feasible possibilities are smoothly defined by finite numbers of equality and inequality constraints, then one can use a number of sophisticated methods to identify local solutions, that is, possibilities that are as good or better than any other nearby possibilities. However, finding global solutions is much harder.