APPROXIMATE SOLUTIONS IN NONSMOOTH ROBUST OPTIMIZATION WITH LOCALLY LIPSCHITZ CONSTRAINTS

摘要

In this paper, we consider a robust optimization problem with locally Lipschitz constraints, and study some characterizations of a so-called quasi epsilon-solution in this setting. In other words, a necessary optimality condition for a quasi epsilon-solution to the mentioned problem is established under some suitable robust constraint qualification; sufficient optimality conditions are also provided with the help of generalized convexity. The optimality conditions are presented in terms of multipliers and limiting subdifferentials of the related functions. Moreover, a simple example is provided to illustrate necessary optimality conditions. Finally, approximate duality relationships are discussed after a Wolfe type dual model (in approximate form) is formulated.