In this paper, we study a first-order solution method for a particular class of set optimization problems where the solution concept is given by the set approach. We consider the case in which the set-valued objective mapping is identified by a finite number of continuously differentiable selections. The corresponding set optimization problem is then equivalent … Read more
This paper studies the fundamental vessel deployment problem in the liner shipping industry, which decides the numbers of mixed-type ships and their sailing frequencies on fixed routes to provide sufficient vessel capacity for fulfilling stochastic shipping demands with high probability. In reality, it is usually difficult (if not impossible) to acquire a precise joint distribution … Read more
We present GALINI, an open source solver for nonconvex mixed-integer quadratically-constrained quadratic programs formulated with the Python algebraic modeling library Pyomo. GALINI uses Pyomo to represent optimization problems and leverages the existing library ecosystem to implement different parts of the solver. GALINI includes a generic branch \& bound algorithm that can be use develop new … Read more
We study different classes of convex and quasiconvex set-valued maps defined by means of the lower-less order relation and the upper-less order relation. The aim of this paper is to formulate necessary and especially sufficient conditions for the convexity/quasiconvexity of extremal value functions. CitationDOI: 10.23952/asvao.3.2021.3.04ArticleDownload View PDF
The moment sum of squares (moment-SOS) hierarchy produces sequences of upper and lower bounds on functionals of the exit time solution of a polynomial stochastic differential equation with polynomial constraints, at the price of solving semidefinite optimization problems of increasing size. In this note we use standard results from elliptic partial differential equation analysis to … Read more
Optimization problems with discrete decisions are nonconvex and thus lack strong duality, which limits the usefulness of tools such as shadow prices. It was shown in Burer (2009) that mixed-binary quadratic programs can be written as completely positive programs, which are convex. We apply this perspective by writing unit commitment in power systems as a … Read more
In this paper, we show how to efficiently schedule the Brazilian OR conference using a matheuristic approach. The event has traditionally around 300 presentations across a period of 3 to 4 days, and building a schedule for the technical sessions is an arduous task. The proposed algorithm integrates the concepts of iterated local search and … Read more
The exponential function and its logarithmic counterpart are essential corner stones of nonlinear mathematical modeling. In this paper we treat their conic extensions, the exponential cone and the relative entropy cone, in primal, dual and polar form, and show that finding the nearest mapping of a point onto these convex sets all reduce to a … Read more
Decision making problems are typically concerned with maximizing efficiency. In contrast, we address problems where there are multiple stakeholders and a centralized decision maker who is obliged to decide in a fair manner. Different decisions give different utility to each stakeholder. In cases where these decisions are made repeatedly, we provide efficient mathematical programming formulations … Read more
In the daily dispatching of urban deliveries, a delivery manager has to consider workload balance among the couriers to maintain workforce morale. We consider two types of workload: incentive workload, which relates to the delivery quantity and affects a courier’s income, and effort workload, which relates to the delivery time and affects a courier’s health. … Read more