On the Mathematical Foundations of Nondifferentiable Optimization in Engineering Design

It is shown by example that a large class of engineering design problems can be transcribed into the form of a canonical optimization problem with inequality constraints involving mar functions. Such problems are commonly referred to as semi-infinite optimization problems. The bulk of this paper is devoted to the development of a mathematical theory for the construction of first order nondifferentiable optimization algorithms, related to phase I - phase II methods of feasible directions, which solve these semi-infinite optimization problems. The applicability of the theory is illustrated with examples that are relevant to engineering design.