Miguel A. Lejeune

A Solution Method for Single-Source Capacitated Facility Location Problems Under Decision-Dependent Demand

Categories Combinatorial Optimization, Stochastic Programming Tags , ,

We present a model and an exact solution method for single-source capacitated facility location problems with decision-dependent demand uncertainty. The model allows the joint probability distribution of customer demands to depend on the facility to which demand points are allocated. The number of possible decision-dependent distributions is therefore equal to the number of feasible allocations … Read more

Dantzig-Wolfe Decomposition for Monotone Two-Stage Stochastic Mixed-Integer Programs Applied to a Power Distribution System Resilience Problem

Categories Stochastic Programming Tags , , , , ,

We develop a novel Dantzig-Wolfe (DW) decomposition algorithm for monotone two-stage stochastic mixed-integer programs (SMIPs). The key novelty in this algorithm is to relax the non-anticipativity constraints (NACs) in line with the monotonicity in the problem. We prove (i) that the relaxed restricted master problem (RMP) faster identifies dominated columns that cannot improve the RMP … Read more

A Successive Proximal DC Penalty Method with an Application to Mathematical Programs with Complementarity Constraints

Categories Bilevel Optimization, Constrained Nonlinear Optimization, Global Optimization Tags , , , ,

We develop a successive, proximal difference-of-convex (DC) function penalty method for solving DC programs with DC constraints. The proposed approach relies on a DC penalty function that measures the violation of constraints and leads to a penalty reformulation sharing the same solution set as the original problem. The resulting penalty problem is a DC program … Read more

A Heuristic for Complementarity Problems Using Difference of Convex Functions

Categories Complementarity and Variational Inequalities Tags , , , ,

We present a new difference of convex functions algorithm (DCA) for solving linear and nonlinear mixed complementarity problems (MCPs). The approach is based on the reformulation of bilinear complementarity constraints as difference of convex (DC) functions, more specifically, the difference of scalar, convex quadratic terms. This reformulation gives rise to a DC program, which is … Read more

Distributionally Robust Optimization under Decision-Dependent Ambiguity Set with an Application to Machine Scheduling

Categories Scheduling, Stochastic Programming

We introduce a new class of distributionally robust optimization problems under decision dependent ambiguity sets. In particular, as our ambiguity sets, we consider balls centered on a decision-dependent probability distribution. The balls are based on a class of earth mover’s distances that includes both the total variation distance and the Wasserstein metrics. We discuss the … Read more

A Framework for Solving Chance-Constrained Linear Matrix Inequality Programs

Categories Stochastic Programming Tags , , , ,

We propose a novel partial sample average approximation (PSAA) framework to solve the two main types of chance-constrained linear matrix inequality (CCLMI) problems: CCLMI with random technology matrix, and CCLMI with random right-hand side. We propose a series of computationally tractable PSAA-based approximations for CCLMI problems, analyze their properties, and derive sufficient conditions ensuring convexity. … Read more

Distributionally Robust Optimization with Decision-Dependent Ambiguity Set

Categories Stochastic Programming

We introduce a new class of distributionally robust optimization problems under decision-dependent ambiguity sets. In particular, as our ambiguity sets we consider balls centered on a decision-dependent probability distribution. The balls are based on a class of earth mover’s distances that includes both the total variation distance and the Wasserstein metrics. We discuss the main … Read more

Data-Driven Distributionally Robust Chance-Constrained Optimization with Wasserstein Metric

Categories Robust Optimization, Second-Order Cone Programming, Stochastic Programming Tags , ,

We study distributionally robust chance-constrained programming (DRCCP) optimization problems with data-driven Wasserstein ambiguity sets. The proposed algorithmic and reformulation framework applies to distributionally robust optimization problems subjected to individual as well as joint chance constraints, with random right-hand side and technology vector, and under two types of uncertainties, called uncertain probabilities and continuum of realizations. … Read more

Risk-based Loan Pricing: Portfolio Optimization Approach With Marginal Risk Contribution

Categories (Mixed) Integer Nonlinear Programming, Finance and Economics, Stochastic Programming Tags , , , , , , ,

We consider a lender (bank) who determines the optimal loan price (interest rates) to offer to prospective borrowers under uncertain risk and borrowers’ response. A borrower may or may not accept the loan at the price offered, and in the presence of default risk, both the principal loaned and the interest income become uncertain. We … Read more

Data-Driven Optimization of Reward-Risk Ratio Measures

Categories Finance and Economics, Stochastic Programming Tags , , , , ,

We investigate a class of fractional distributionally robust optimization problems with uncertain probabilities. They consist in the maximization of ambiguous fractional functions representing reward-risk ratios and have a semi-infinite programming epigraphic formulation. We derive a new fully parameterized closed-form to compute a new bound on the size of the Wasserstein ambiguity ball. We design a … Read more