2019/02/05 by Patrick Mehlitz, Mehlitz, Patrick · 1 citation
Computer Science · Engineering · Mathematics · #90C30 #90C33 #Advanced Optimization Algorithms Research #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Mathematical Programming #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.1902.01614
openalex publication_date 2019/02/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Mathematical programs with disjunctive constraints (MPDCs for short) cover\nseveral different problem classes from nonlinear optimization including\ncomplementarity-, vanishing-, cardinality-, and switching-constrained\noptimization problems. In this paper, we introduce an abstract but reasonable\nversion of the prominent linear independence constraint qualification which\napplies to MPDCs. Afterwards, we derive first- and second-order optimality\nconditions for MPDCs under validity of this constraint qualification based on\nso-called strongly stationary points. Finally, we apply our findings to some\npopular classes of disjunctive programs and compare the obtained results to\nthose ones available in the literature. Particularly, new second-order\noptimality conditions for mathematical programs with switching constraints are\nby-products of our approach.\n