We consider the situation that the grand set of all players, in a cooperative game in characteristic function form with a nonempty core, consists of recognizable subsets of players. The underlying assumption is that the players of each subset have something in common between themselves which is not shared by the players of other subsets. … Read more
We prove that deciding whether an integer cubic polynomial takes a value at most one over three nonnegative integers is NP-hard. Hardness holds even when every feasible objective value is a positive integer, so every constructed instance has a finite, attained minimum. This establishes a sharp dimension boundary for the tractability of cubic integer optimization … Read more
Explainability is a growing concern for optimization models used as decision-making tools. It aims to help a stakeholder understand why a model recommends a given outcome, typically by exhibiting the elements of the input that account for this outcome. We study this question for linear two-stage stochastic programs, and explain the returned decision by a … Read more
Kuhn-Tucker (KT) demand models characterize consumers’ budget allocation through the Karush-Kuhn-Tucker conditions of utility maximization. Classical specifications, including quadratic utility, are widely used to study pricing, assortment, and competition, but remain difficult to estimate from consumer data. By contrast, models designed for tractable estimation often impose restrictive assumptions on demand behavior. We address this gap … Read more
We study a non-contiguous channelisation problem arising in multi-beam geostationary satellite communications. Carriers have heterogeneous sub- channel demands and priorities; carriers within the same beam cannot share a subchannel, while reuse across beams is permitted subject to carrier- specific cumulative-interference budgets. Demand may be partially satis- fied, with a priority-weighted objective favouring higher-priority tra!c when … Read more
Trust-region methods are fundamental to nonlinear optimization, but solving the trust-region subproblem exactly can be computationally expensive. This paper proposes Aries, a three-segment path approximation that extends the classical dogleg path while retaining comparable per-iteration work. We state the assumptions under which the usual trust-region sufficient-decrease argument applies and describe an adaptive rule for selecting … Read more
Distributionally robust optimization (DRO) minimizes worst-case risk under distributional uncertainty, but its decisions can be suboptimal in terms of their excess risk, or regret. We study this gap for multivariate least-squares regression, assuming that the observed source law and unknown target law differ by an adversarial 2-Wasserstein perturbation of size \(\varepsilon\). We first identify the … Read more
Classic linear bilevel optimization assumes that the upper-level decision impacts only the right-hand side of the lower-level constraints, which guarantees a solution under mild conditions. We study existence of solutions for linear bilevel problems with rotations (LBPR, for short), i.e., problems for which the upper-level decision modifies the left-hand side coefficients of the linear follower … Read more
We introduce quasinormality and pseudonormality for nonlinear second-order cone programming by exploiting the spectral geometry of the Lorentz cone. The proposed quasinormality distinguishes interior and boundary multipliers and, in the latter case, relates constraint violation to the corresponding spectral direction. It recovers classical quasinormality when all cone blocks are one-dimensional and is strictly weaker than … Read more
Performative decision-making arises in many real-world problems where decisions influence the populations that generate future data. A major line of existing research focuses on learning performatively stable solutions. We study average-reward performative optimization, where the learner observes an evolving population through sample batches of fixed size and learns from a single continuing trajectory with unknown … Read more