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Gradient Formulae for Nonlinear Probabilistic Constraints with Non-convex Quadratic Forms

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  • Wim Ackooij

    (Électricité de France - EDF R&D)

  • Pedro Pérez-Aros

    (Universidad de O’Higgins)

Abstract

Probability functions appearing in chance constraints are an ingredient of many practical applications. Understanding differentiability, and providing explicit formulae for gradients, allow us to build nonlinear programming methods for solving these optimization problems from practice. Unfortunately, differentiability of probability functions cannot be taken for granted. In this paper, motivated by gas network applications, we investigate differentiability of probability functions acting on non-convex quadratic forms. We establish continuous differentiability for the broad class of elliptical random vectors under mild conditions.

Suggested Citation

  • Wim Ackooij & Pedro Pérez-Aros, 2020. "Gradient Formulae for Nonlinear Probabilistic Constraints with Non-convex Quadratic Forms," Journal of Optimization Theory and Applications, Springer, vol. 185(1), pages 239-269, April.
    • Handle: RePEc:spr:joptap:v:185:y:2020:i:1:d:10.1007_s10957-020-01634-9
    DOI: 10.1007/s10957-020-01634-9
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    References listed on IDEAS

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    Cited by:

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