Variational Analysis in Semi-Infinite and Infinite Programming, II: Necessary Optimality Conditions

This paper concerns applications of advanced techniques of variational analysis and generalized differentiation to problems of semi-infinite and infinite programming with feasible solution sets defined by parameterized systems of infinitely many linear inequalities of the type intensively studied in the preceding development [Cánovas et al., SIAM J. Optim., 20 (2009), pp. 1504–1526] from the viewpoint of robust Lipschitzian stability. The main results establish necessary optimality conditions for broad classes of semi-infinite and infinite programs, where objectives are generally described by nonsmooth and nonconvex functions on Banach spaces and where infinite constraint inequality systems are indexed by arbitrary sets. The results obtained are new in both smooth and nonsmooth settings of semi-infinite and infinite programming. We illustrate our model and results by considering a practically meaningful model of water resource optimization via systems of reservoirs.This research was partially supported by grants MTM2008-06695-C03 (01-02) from MICINN (Spain), ACOMP/2009/047&133, and ACOMP/2010/269 from Generatitat Valenciana (Spain)