Optimality conditions in convex semi-infinite optimization. An approach based on the subdifferential of the supremum function

Abstract: We present a survey on optimality conditions (of Fritz-John and KKT-type) for semi-infinite convex optimization problems. The methodology is based on the use of the subdifferential of the supremum of the infinite family of constraint functions. Our approach aims to establish weak constraint qualifications and, in the last step, to dropp out the usual continuity/closedness assumptions which are standard in the literature. The material in this survey is extracted from the following papers:

R. Correa, A. Hantoute, M. A. López, Weaker conditions for subdifferential calculus of convex functions. J. Funct. Anal. 271 (2016), 1177-1212.

R. Correa, A. Hantoute, M. A. López, Moreau-Rockafellar type formulas for the subdifferential of the supremum function. SIAM J. Optim. 29 (2019), 1106-1130.

R. Correa, A. Hantoute, M. A. López, Valadier-like formulas for the supremum function II: the compactly indexed case. J. Convex Anal. 26 (2019), 299-324.

R. Correa, A. Hantoute, M. A. López, Subdifferential of the supremum via compactification of the index set. To appear in Vietnam J. Math. (2020).

optimization and control

Audience: researchers in the topic

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