Nonlinear Stochastic Programming Involving CVaR in the Objective and Constraints

Abstract. The nonlinear stochastic programming problem involving CVaR in the objective and constraints is considered. Solving the latter problem in a framework of bi-level stochastic programming, the extended Lagrangian is introduced and the related KKT conditions are derived. Next, the sequential simulation-based approach has been developed to solve stochastic problems with CVaR by finite sequences of Monte Carlo samples. The approach considered is grounded by the rule for iterative regulation of the Monte Carlo sample size and the stochastic termination procedure, taking into account the stochastic model risk. The rule is introduced to regulate the size of the Monte Carlo sample inversely proportionally to the square of the stochastic gradient norm allows us to solve stochastic nonlinear problems in a rational way and ensures the convergence. The proposed termination procedure enables us to test the KKT conditions in a statistical way and to evaluate the confidence intervals of the...

• Type: Journal
• Year: 2016
• Where: INFORMATICALT
• Authors: Valerijonas Dumskis, Leonidas Sakalauskas
• Keywords: INFORMATICALT 2016, Software Engineering