On the linear independence constraint qualification in disjunctive programming. (2nd October 2020)

• Record Type: Journal Article
• Authors: Mehlitz, Patrick
• Is Part Of: Optimization. Volume 69:Number 10(2020)
• Page Start: 2241
• Page End: 2277
• Publication Date: 2020-10-02
• Subjects: Constraint qualifications -- disjunctive programming -- linear independence constraint qualification -- strong stationarity -- second-order optimality conditions; 90C30 -- 90C33; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2019.1679811
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : Mathematical programmes with disjunctive constraints (MPDCs for short) cover several different problem classes from nonlinear optimization including complementarity-, vanishing-, cardinality- and switching-constrained optimization problems. In this paper, we introduce an abstract but reasonable version of the prominent linear independence constraint qualification which applies to MPDCs. Afterwards, we derive first- and second-order optimality conditions for MPDCs under validity of this constraint qualification based on so-called strongly stationary points. Finally, we apply our findings to some popular classes of disjunctive programmes and compare the obtained results to those ones available in the literature. Particularly, new second-order optimality conditions for mathematical programmes with switching constraints are by-products of our approach.