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

Wim Ackooij () and Pedro Pérez-Aros ()
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Wim Ackooij: Électricité de France - EDF R&D
Pedro Pérez-Aros: Universidad de O’Higgins

Journal of Optimization Theory and Applications, 2020, vol. 185, issue 1, No 14, 239-269

Abstract: 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.

Keywords: Stochastic optimization; Probabilistic constraints; Chance constraints; Gradients of probability functions; 90C15 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10957-020-01634-9

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