Fast Feasible Direction Methods, with Engineering Applications

Optimization problems arising in engineering applications often present distinctive features that are not exploited, or not accounted for, in standard numerical optimization algorithms and software codes. First, in many cases, equality constraints are not present, or can be simply eliminated. Second, there are several instances where it is advantageous, or even crucial, that, once a feasible point has been achieved, all subsequent iterates be feasible as well. Third, many optimization problems arising engineering are best formulated as constrained minimax problems. Fourth, some specifications must be achieved over a range of values of an independent parameter (functional constraints).While various other distinctive features arise in optimization problems found in specific classes of engineering problems, this paper focuses on those identified above, as they have been the object of special attention by the authors and their co-workers in recent years. Specifically, a basic scheme for efficiently tackling inequality constrained optimization while forcing feasible iterates is discussed and various extensions are proposed to handle the distinctive features just pointed out