Nonlinear Chance Constrained Problems: Optimality Conditions, Regularization and Solvers

0460909 - ÚTIA 2017 RIV US eng J - Článek v odborném periodiku
Adam, Lukáš - Branda, Martin
Nonlinear Chance Constrained Problems: Optimality Conditions, Regularization and Solvers.
Journal of Optimization Theory and Applications. Roč. 170, č. 2 (2016), s. 419-436. ISSN 0022-3239. E-ISSN 1573-2878
Grant CEP: GA ČR GA15-00735S
Institucionální podpora: RVO:67985556
Klíčová slova: Chance constrained programming * Optimality conditions * Regularization * Algorithms * Free MATLAB codes
Kód oboru RIV: BB - Aplikovaná statistika, operační výzkum
Impakt faktor: 1.289, rok: 2016
http://library.utia.cas.cz/separaty/2016/MTR/adam-0460909.pdf

We deal with chance constrained problems with differentiable nonlinear random functions and discrete distribution. We allow nonconvex functions both in the constraints and in the objective. We reformulate the problem as a mixed-integer nonlinear program and relax the integer variables into continuous ones. We approach the relaxed problem as a mathematical problem with complementarity constraints and regularize it by enlarging the set of feasible solutions. For all considered problems, we derive necessary optimality conditions based on Fréchet objects corresponding to strong stationarity. We discuss relations between stationary points and minima. We propose two iterative algorithms for finding a stationary point of the original problem. The first is based on the relaxed reformulation, while the second one employs its regularized version.
Trvalý link: http://hdl.handle.net/11104/0261533