A tractable approximation of non-convex chance constrained optimization with non-Gaussian uncertainties

作者：Geletu Abebe^*; Kloeppel Michael; Hoffmann Armin; Li Pu

来源：Engineering Optimization, 2015, 47(4): 495-520.

DOI：10.1080/0305215X.2014.905550

• analytic approximation
• non-Gaussian distribution
• non-convex optimization
• chance constraints

Chance constrained optimization problems in engineering applications possess highly nonlinear process models and non-convex structures. As a result, solving a nonlinear non-convex chance constrained optimization (CCOPT) problem remains as a challenging task. The major difficulty lies in the evaluation of probability values and gradients of inequality constraints which are nonlinear functions of stochastic variables. This article proposes a novel analytic approximation to improve the tractability of smooth non-convex chance constraints. The approximation uses a smooth parametric function to define a sequence of smooth nonlinear programs (NLPs). The sequence of optimal solutions of these NLPs remains always feasible and converges to the solution set of the CCOPT problem. Furthermore, Karush-Kuhn-Tucker (KKT) points of the approximating problems converge to a subset of KKT points of the CCOPT problem. Another feature of this approach is that it can handle uncertainties with both Gaussian and/or non-Gaussian distributions.

• 出版日期2015-4-3