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Nonlinear Chance Constrained Problems: Optimality Conditions, Regularization and Solvers

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    0460909 - ÚTIA 2017 RIV US eng J - Journal Article
    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
    R&D Projects: GA ČR GA15-00735S
    Institutional support: RVO:67985556
    Keywords : Chance constrained programming * Optimality conditions * Regularization * Algorithms * Free MATLAB codes
    Subject RIV: BB - Applied Statistics, Operational Research
    Impact factor: 1.289, year: 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.
    Permanent Link: http://hdl.handle.net/11104/0261533

     
     
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