The stable set problem admits various binary linear and quadratic formulations. The Shor relaxation of a particular quadratic formulation is the well-known theta body. We consider aggregations of quadratic constraints of this formulation, yielding exact and inexact quadratic formulations of the stable set problem, and then establish conditions under which the aggregated quadratic formulation is … Read more
We develop a symmetry-compatible framework for first-order methods on matrix optimization problems. The central principle is that the update rule for a matrix variable should be equivariant with respect to the natural symmetry group acting on that variable. For matrix representations of linear operators, this leads to bi-orthogonal equivariance under left and right orthogonal changes … Read more
Residential parcel lockers (RPLs), unlike their public counterparts, facilitate secure parcel delivery to occupants of private apartment and condominium buildings in urban areas. In this work, we consider the perspective of a last-mile parcel carrier that has access to an RPL in the lobby of a high-rise residential building. Motivated by growing e-commerce demand, we … Read more
Optimization models are built in a variety of modeling languages and solved by a variety of solvers, but once a solution exists, the information needed to understand it is fragmented: each solver exposes a partial, differently named set of native diagnostics, and the modeling language has already canonicalized the formulation the user wrote. We present … Read more
Classical optimization methods determine a single optimal or near-optimal solution for a decision problem. In many applications, however, the decision maker is interested in evaluating a pool of high-quality solutions, to encode fairness-oriented criteria or to obtain a portfolio of alternatives to use in case of unexpected scenarios. In this paper, we consider the problem … Read more
Risk-averse distributionally robust multi-item newsvendor problems provide a fundamental model for inventory decisions under demand uncertainty, limited distributional information, and downside-risk concerns. We study this problem under mean-covariance demand ambiguity, where the decision maker maximizes the worst-case conditional value-at-risk of profit. While cross-item demand correlations are important for portfolio-level inventory decisions, they are difficult to … Read more
Azuma, Kim, and Yamashita formulated the verification problem for one-layer ReLU networks as a quadratically constrained quadratic program and established tight semidefinite relaxations for the edgeless case and for one-unit settings. In this work, we represent the sharing pattern of undecided ReLUs over a box input set through an input-sharing graph and focus on the … Read more
The length-constrained cycle partition problem (LCCP) is a graph optimization problem in which a set of nodes must be partitioned into a minimum number of cycles. Every node is associated with a critical time and the length of every cycle must not exceed the critical time of any node in the cycle. We formulate LCCP … Read more
We study energy-efficient operation of underground train networks, where energy from regenerative braking is usable only if another train in the same electrically isolated subnetwork accelerates simultaneously. Timetabling models for this setting typically fix one velocity profile per leg and running time, which limits the matching of braking and accelerating phases. We drop this assumption … Read more
Imagine that you are in front of a cockpit with several on–off buttons. If you were to thoroughly test it, you would need to try a prohibitive number of configurations. But since most bugs in practice can be isolated to interactions among few components, having tests that cover every possible pairwise configuration is a good … Read more