Abstract Bilevel optimization is an increasingly important tool to model hierarchical decision making. However, the ability of modeling such settings makes bilevel problems hard solve in theory and practice. In this paper, we add on general difficulty class by further incorporating convex black-box constraints lower level. For setup, develop a cutting-plane algorithm that computes approximate b...

In this paper, we address the problem of maximizing expected return subject to a worst case return constraint by composing a portfolio that may consist of cash, holdings in a stock market index and options on the index. We derive properties of optimal and feasible portfolios and present a linear programming model to solve the problem. The optimal portfolios have pay-off functions that reflect a...

This paper is concerned with chance constrained programming to deal with nonlinear optimization problems with random parameters. Specific Monte Carlo methods to evaluate the gradient and Hessian of probabilistic constraints are proposed and discussed. These methods are implemented in penalization optimization routines adapted to stochastic optimization. They are shown to reduce the computationa...

This paper addresses a chance-constrained model predictive control (CC-MPC) strategy for the management of drinking water networks (DWNs) based on a finite horizon stochastic optimisation problem with joint probabilistic (chance) constraints. In this approach, water demands are considered additive stochastic disturbances with non-stationary uncertainty description, unbounded support and known (...