This study addresses the bilevel discrete network design problem (DNDP) with congestion, with special emphasis on fairness. The upper-level decision-maker (the 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. Most … 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
Problem definition: To collect data on ocean plastic pollution and build more accurate predictive models, we need to manually take high-resolution pictures of the sea surface via floating or flying drones. Operating these vehicles, like many data collection problems in agriculture or environmental science, challenges the traditional optimal experimental design (OED) formulation from statistics by … Read more
We consider a capacitated location-allocation-pricing problem in a single-commodity supply chain with stochastic price-sensitive demands, where the location, allocation and pricing decisions are made simultaneously. Under a general risk measure representing an arbitrary risk tolerance policy, the problem is modeled as a two-stage stochastic mixed-integer program with a translation-invariant monotone risk measure. To solve the … Read more
We are concerned with contingent derivatives and their second-order counterparts (introduced by Ngai et al.) of set-valued mappings. Special attention is given to the development of new sum-rules for second-order contingent derivatives. To be precise, we want to find conditions under which the second-order contingent derivative of the sum of a smooth and a set-valued … Read more