This paper introduces a spatial branch-and-bound method for the approximate computation of the set of all epsilon-Nash equilibria of continuous box-constrained non-convex Nash equilibrium problems. We explain appropriate discarding and fathoming techniques, provide a termination proof for a prescribed approximation tolerance, and report our computational experience. ArticleDownload View PDF
Multiobjective quadratic programs (MOQPs) are appealing since convex quadratic programs have elegant mathematical properties and model important applications. Adding mixed-integer variables extends their applicability while the resulting programs become global optimization problems. We design and implement a branch and bound (BB) algorithm for biobjective mixed-integer quadratic programs (BOMIQPs). In contrast to the existing algorithms in … Read more
Truck-and-drone routing problems have become an important topic of research in the last decade due to their applications for last-mile deliveries. Despite the large number of publications in this area, the most efficient exact algorithms designed thus far struggle to solve the benchmark instances with 39 or more customers. This fact is true even for … Read more
We study multistage distributionally robust linear optimization, where the uncertainty set is defined as a ball of distribution centered at a scenario tree using the nested distance. The resulting minimax problem is notoriously difficult to solve due to its inherent non-convexity. In this paper, we demonstrate that, under mild conditions, the robust risk evaluation of … Read more
In this paper we propose a spectral Fletcher-Reeves conjugate gradient-like method (SFRCG) for solving unconstrained bi-criteria minimisation problems without using any technique of scalarization. We suggest an explicit formulae for computing a descent direction common to both criteria. This latter verifies furthermore a sufficient descent property which does not depend on the line search nor … Read more
We establish the weak convergence of inertial Krasnoselskii-Mann iterations towards a common fixed point of a family of quasi-nonexpansive operators, along with worst case estimates for the rate at which the residuals vanish. Strong and linear convergence are obtained in the quasi-contractive setting. In both cases, we highlight the relationship with the non-inertial case, and … Read more
We consider the bilevel knapsack problem with interdiction constraints, a fundamental bilevel integer programming problem which generalizes the 0-1 knapsack problem. In this problem, there are two knapsacks and \(n\) items. The objective is to select some items to pack into the first knapsack such that the maximum profit attainable from packing some of the … Read more
This paper focuses on algorithms for multi-stage stochastic linear programming (MSLP). We propose an ensemble method named the “compromise policy”, which not only reduces the variance of the function approximation but also reduces the bias of the estimated optimal value. It provides a tight lower bound estimate with a confidence interval. By exploiting parallel computing, … Read more
A common strategy for solving an unconstrained two-player Nash equilibrium problem with continuous variables is applying Newton’s method to the system of nonlinear equations obtained by the corresponding first-order necessary optimality conditions. However, when taking into account the game dynamics, it is not clear what is the goal of each player when considering that they … Read more
For many developing countries, COVID-19 vaccination roll-out programs are not only slow but vaccination centers are also exposed to the risk of natural disaster, like flooding, which may slow down vaccination progress even further. Policy-makers in developing countries therefore seek to implement strategies that hedge against distribution risk in order for vaccination campaigns to run … Read more