Being inspired by the parametric decomposition theorem for multiobjective optimization problems (MOPs) of Cuenca Mira and Miguel García (2017), and by the block-coordinate descent for single objective optimization problems, we present a decomposition theorem for computing the set of minimal elements of a partially ordered set. This set is decomposed into subsets whose minimal elements … Read more
In this paper, we address a challenging problem faced by a Brazilian oil and gas company regarding the rescheduling of helicopter flights from an onshore airport to maritime units, crucial for transporting company employees. The problem arises due to unforeseen events like bad weather or mechanical failures, leading to delays or postponements in the original … Read more
Active research on optimal control methods comprises the developments of research groups from various fields, including control, mathematics, and process systems engineering. Although there is a consensus on the classification of the main solution methods, different terms are often used for the same method. For example, solving optimal control problems with control discretization and embedded … Read more
This study addresses the bilevel network design problem (NDP) with congestion. The upper-level decision-maker (a network designer) selects a set of arcs to add to an existing transportation network, while the lower-level decision-makers (drivers) respond by choosing routes that minimize their individual travel times, resulting in user equilibrium. In this work, we propose two novel … Read more
A Surgery Pre-Admission Testing (PAT) clinic is a hospital unit designed to serve pre-operative patients by gathering critical patient information and performing procedure-specific tests to prepare them for surgery. Patients may require multiple tests, each conducted by a specialized nurse. A patient must be assigned to a room before starting any test and must stay … Read more
We study offline reinforcement learning problems with a long-run average reward objective. The state-action pairs generated by any fixed behavioral policy thus follow a Markov chain, and the empirical state-action-next-state distribution satisfies a large deviations principle. We use the rate function of this large deviations principle to construct an uncertainty set for the unknown true … Read more
Graphons generalize graphs and define a limit object of a converging graph sequence. The notion of graphons allows for a generic representation of coupled network dynamical systems. We are interested in approximating integer controls for graphon dynamical systems. To this end, we apply a decomposition approach comprised of a relaxation and a reconstruction step. We … Read more
This paper considers convex quadratic programs associated with the training of support vector machines (SVM). Exploiting the special structure of the SVM problem a new type of active set method with long cycles and stable rank-one-updates is proposed and tested (CMU: cycling method with updates). The structure of the problem allows for a repeated simple … Read more
This paper proposes a universal, optimal algorithm for convex minimization problems of the composite form $g_0(x)+h(g_1(x),\dots, g_m(x)) + u(x)$. We allow each $g_j$ to independently range from being nonsmooth Lipschitz to smooth, from convex to strongly convex, described by notions of H\”older continuous gradients and uniform convexity. Note that, although the objective is built from … Read more
The Lyapunov rank of a cone is the dimension of the Lie algebra of its automorphism group. It is invariant under linear isomorphism and in general not unique—two or more non-isomorphic cones can share the same Lyapunov rank. It is therefore not possible in general to identify cones using Lyapunov rank. But suppose we look … Read more