2016/11/24 by Matúš Benko, Benko, Matúš, Helmut Gfrerer +1
Computer Science · Mathematics · Engineering · #Optimization and Variational Analysis #Advanced Optimization Algorithms Research #Advanced Control Systems Optimization
paper · pdf · doi:10.48550/arxiv.1611.08206
In this paper we consider a sufficiently broad class of nonlinear\nmathematical programs with disjunctive constraints, which, e.g., include\nmathematical programs with complemetarity/vanishing constraints. We present an\nextension of the concept of mathcal Q-stationarity as introduced in the\nrecent paper [2]. mathcal Q-stationarity can be easily combined with the\nwell-known notion of M-stationarity to obtain the stronger property of\nso-called mathcal QM-stationarity. We show how the property of mathcal\nQM-stationarity (and thus also of M-stationarity) can be efficiently\nverified for the considered problem class by computing mathcal\nQ-stationary solutions of a certain quadratic program. We consider further\nthe situation that the point which is to be tested for mathcal\nQM-stationarity, is not known exactly, but is approximated by some\nconvergent sequence, as it is usually the case when applying some numerical\nmethod.\n