Global Solution of Semi-infinite Programs with Existence Constraints

Abstract We consider what we term existence-constrained semi-infinite programs. They contain a finite number of (upper-level) variables, regular objective, and existence constraints. These constraints assert that for all (medial-level) variable values from set infinite cardinality, there must exist (lower-level) second satisfy an inequality. Existence-constrained programs are generalization programs, possess three rather than two levels, found in applications. Building on our previous work the global solution (Djelassi Mitsos J Glob Optim 68(2):227–253, 2017), propose (for first time) algorithm absent any convexity or concavity assumptions. The is guaranteed to terminate with globally optimal feasibility under assumptions similar ones made case. In particular, it assumed host sets compact, defining functions continuous, appropriate nonlinear programming subsolver used, exists Slater point respect A proof termination provided. Numerical results provided adjustable robust design problem chemical engineering literature.