Generalized semi-infinite optimization: a first order optimality condition and examples
Mathematical Programming: Series A and B
BI-Level Strategies in Semi-Infinite Programming
BI-Level Strategies in Semi-Infinite Programming
Lagrange Multipliers in Nonsmooth Semi-Infinite Optimization Problems
Mathematics of Operations Research
Metric Regularity in Convex Semi-Infinite Optimization under Canonical Perturbations
SIAM Journal on Optimization
SIAM Journal on Optimization
Mathematical Programming: Series A and B - Series B - Special Issue: Well-posedness, stability and related topics
Fréchet subdifferentials of efficient point multifunctions in parametric vector optimization
Journal of Global Optimization
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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.