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Journal Article

Nonlinear Chance Constrained Problems: Optimality Conditions, Regularization and Solvers

Adam Lukáš, Branda Martin

: Journal of Optimization Theory and Applications vol.170, 2 (2016), p. 419-436

: GA15-00735S, GA ČR

: Chance constrained programming, Optimality conditions, Regularization, Algorithms, Free MATLAB codes

: 10.1007/s10957-016-0943-9

: http://library.utia.cas.cz/separaty/2016/MTR/adam-0460909.pdf

(eng): 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.

: BB