New verifiable stationarity concepts for a class of mathematical programs with disjunctive constraints. (2nd January 2018)

• Record Type: Journal Article
• Authors: Benko, Matúš; Gfrerer, Helmut
• Is Part Of: Optimization. Volume 67:Number 1(2018)
• Page Start: 1
• Page End: 23
• Publication Date: 2018-01-02
• Subjects: Mathematical programs with disjunctive constraints -- B-stationarity -- M-stationarity -- -stationarity; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2017.1387547
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract: In this paper, we consider a sufficiently broad class of non-linear mathematical programs with disjunctive constraints, which, e.g. include mathematical programs with complemetarity/vanishing constraints. We present an extension of the concept of -stationarity which can be easily combined with the well-known notion of M-stationarity to obtain the stronger property of so-called -stationarity. We show how the property of -stationarity (and thus also of M-stationarity) can be efficiently verified for the considered problem class by computing -stationary solutions of a certain quadratic program. We consider further the situation that the point which is to be tested for -stationarity, is not known exactly, but is approximated by some convergent sequence, as it is usually the case when applying some numerical method.