This study examines a resource-sharing problem involving multiple parties that agree to use a set of capacities together. We start with modeling the whole problem as a mathematical program, where all parties are required to exchange information to obtain the optimal objective function value. This information bears private data from each party in terms of … Read more
This paper considers a generalized form of the standard linear complementarity problem with unique solution and provides a more precise expression of an upper error bound discovered by Chen and Xiang in 2006. This expression has at least two advantages. It makes possible the exact computation of the error bound factor and it provides a … Read more
Full strong-branching (henceforth referred to as strong-branching) is a well-known variable selection rule that is known experimentally to produce significantly smaller branch-and-bound trees in comparison to all other known variable selection rules. In this paper, we attempt an analysis of the performance of the strong-branching rule both from a theoretical and a computational perspective. On … Read more
Planning of trajectories, i.e. paths over time, is a challenging task. Thereby, the trajectories for involved commodities often have to be considered jointly as separation constraints have to be respected. This is for example the case in robot motion or air traffic management. Involving these discrete separation constraints in the planning of best possible continuous … Read more
This paper develops solution strategies for large-scale nonsmooth optimization problems. We transform nonsmooth programs into equivalent mathematical programs with complementarity constraints (MPCCs), and then employ NLP-based strategies for their so- lution. For this purpose, two NLP formulations based on complementarity relaxations are put forward, one of which applies a parameterized formulation and operates with a … Read more
We propose a new variant of Chubanov’s method for solving the feasibility problem over the symmetric cone by extending Roos’s method (2018) of solving the feasibility problem over the nonnegative orthant. The proposed method considers a feasibility problem associated with a norm induced by the maximum eigenvalue of an element and uses a rescaling focusing … Read more
We present an algebraic characterization of perfect graphs, i.e., graphs for which the clique number and the chromatic number coincide for every induced subgraph. We show that a graph is perfect if and only if certain nonnegative polynomials associated with the graph are sums of squares. As a byproduct, we obtain several infinite families of … Read more
In a similar spirit of the extension of the proximal point method developed by Alves et al. \cite{alvegm20}, we propose in this work an Inertial-Relaxed primal-dual splitting method to address the problem of decomposing the minimization of the sum of three convex functions, one of them being smooth, and considering a general coupling subspace. A … Read more
We propose a generic model for the capacitated vehicle routing problem (CVRP) under demand uncertainty. By combining risk measures, satisficing measures or disutility functions with complete or partial characterizations of the probability distribution governing the demands, our formulation bridges the popular but often independently studied paradigms of stochastic programming and distributionally robust optimization. We characterize … Read more
A common approach for minimizing a smooth nonlinear function is to employ finite-difference approximations to the gradient. While this can be easily performed when no error is present within the function evaluations, when the function is noisy, the optimal choice requires information about the noise level and higher-order derivatives of the function, which is often … Read more