The authors consider the following problem:
, is a nonempty subset of , and .
A point is said to be a strict local minimizer of order 1 if there exist and such that
Under weak assumptions on and the , the authors derive a necessary optimality condition for a local minimizer. Moreover, under a certain constraint qualification, a necessary and sufficient condition for a strict local minimizer of order 1 is also established. The optimality conditions are multiplier rules involving Clarke’s generalized gradient.