In this paper, a globally convergent proximal gradient method is developed for convex multi-objective optimization problems using Bregman distance. The proposed method is free from any kind of a priori chosen parameters or ordering information of objective functions. At every iteration of the proposed method, a subproblem is solved to find a descent direction. This … Read more
The graph partition problem (GPP) aims at clustering the vertex set of a graph into a fixed number of disjoint subsets of given sizes such that the sum of weights of edges joining different sets is minimized. This paper investigates the quality of doubly nonnegative (DNN) relaxations, i.e., relaxations having matrix variables that are both … Read more
We propose a new family of formulations with route-based variables for the split delivery vehicle routing problem with and without time windows. Each formulation in this family is characterized by the maximum number of different demand quantities that can be delivered to a customer during a vehicle visit. As opposed to previous formulations in the … Read more
Contraflow means lane reversals on networks. In lane reversal reconfiguration, the capacity of arc increases by reorienting arcs towards demand nodes, which maximizes the flow value and reduces the travel time. In this work, we survey the existing pieces of literature on single and multi-commodity contraflow problems with symmetric and asymmetric travel times on parallel … Read more
In this paper, we consider multistage stochastic variational inequalities (MSVIs). First, we give multistage stochastic programs and multistage multi-player noncooperative game problems as source problems. After that, we derive the monotonicity properties of MSVIs under less restrictive conditions. Finally, the polynomial rate of convergence with respect to sample sizes between the original problem and its … Read more
We propose a new robust actionable prescriptive analytics framework that leverages past data and side information to minimize a risk-based objective function under distributional ambiguity. Our framework aims to find a policy that directly transforms the side information into implementable decisions. Specifically, we focus on developing actionable response policies that offer the benefits of interpretability … Read more
The Resource Constrained Project Scheduling Problem with a flexible Project Structure (RCPSP-PS) is a generalization of the Resource Constrained Project Scheduling Problem (RCPSP). The objective of the RCPSP-PS is to find a minimal makespan schedule subject to precedence and resource constraints, while only having to execute a subset of all activities. We present a general … Read more
This paper presents a fusion of Stochastic Decomposition and the Majorization-Minimization algorithm (SD-MM) to solve a class of non-convex stochastic programs. The objective function is an expectation of a smooth concave function and a second-stage linear recourse function, which is common in stochastic programming (SP). This extension not only allows new stochastic difference-of-convex (dc) functions … Read more
In this paper, we present convergence guarantees for a modified trust-region method designed for minimizing objective functions whose value is computed with noise and for which gradient and Hessian estimates are inexact and possibly random. In order to account for the noise, the method utilizes a relaxed step acceptance criterion and a cautious trust-region radius … Read more
In this work, we propose integral global optimality conditions for multiobjective problems not necessarily differentiable. The integral characterization, already known for single objective problems, are extended to multiobjective problems by weighted sum and Chebyshev weighted scalarizations. Using this last scalarization, we propose an algorithm for obtaining an approximation of the weak Pareto front whose effectiveness … Read more