In this paper, we investigate solution approaches in set optimization that are based on so-called vectorization strategies. Thereby, the original set-valued problems are reformulated as multi-objective optimization problems, whose optimal solution sets approximate those of the original ones in a certain sense. We consider both infinite-dimensional and finite-dimensional vectorization approaches. In doing so, we collect … Read more
This paper presents scalable algorithms for computing pure Nash equilibria (PNEs) in large-scale integer programming games (IPGs), where existing exact methods typically handle only small numbers of players. Motivated by a county-level aquatic invasive species (AIS) prevention problem with 84 decision makers, we develop and analyze random-restart best-response dynamics (RR-BRD), a randomized search framework for … Read more
In this paper, we are concerned with a worst-case complexity analysis of a-posteriori algorithms for unconstrained multiobjective optimization. Specifically, we propose an algorithmic framework that generates sets of points by means of $p$th-order models regularized with a power $p+1$ of the norm of the step. Through a tailored search procedure, several trial points are generated … Read more
We consider unconstrained multi-criteria optimization problems with finite sum objective functions. The proposed algorithm belongs to a non-monotone trust region framework where additional sampling approach is used to govern the sample size and the acceptance of a candidate point. Depending on the problem, the method can yield a mini-batch or an increasing sample size behavior. … Read more
Two-level hierarchical decision-making problems, where a leader’s choice influences a follower’s action, arise across key business and public-sector domains, from market design and pricing to defense. These problems are typically modeled as bilevel programs and are known to be notoriously hard to solve at scale. In single-level combinatorial optimization, especially for challenging instances, local search … Read more
We study the fair and truthful allocation of m divisible public items among n agents, each with distinct preferences for the items. To aggregate agents’ preferences fairly, we focus on finding a core solution. For divisible items, a core solution always exists and can be calculated by maximizing the Nash welfare objective. However, such a … Read more
We study weighted, capacitated cost-sharing games on parallel-link networks, also known as bin packing games. We focus on an integer-splittable variant in which items of varying sizes can be divided into integer units and assigned to bins with heterogeneous capacities and costs. Although this setting has practical relevance, it remains largely unexplored in the context … Read more
We consider Nash equilibrium problems with mixed-integer variables in which each player solves a mixed-integer optimization problem parameterized in the rivals’ strategies. We distinguish between standard Nash equilibrium problems (NEP), where the parameterization acts only on the players’ cost functions and generalized Nash equilibrium problems (GNEPs), where, additionally, the strategy spaces of the players may … Read more
Real world problems often require complex modeling and computation efforts to be effectively addressed. Relying solely on data-driven approaches without integrating physics-based models can result in limited predictive capabilities. Even advanced techniques such as deep learning may be impractical for decision-makers due to the lack of data and challenges in justifying and explaining results. In … Read more
With the success that the field of bilevel optimization has seen in recent years, similar methodologies have started being applied to solving more difficult applications that arise in trilevel optimization. At the helm of these applications are new machine learning formulations that have been proposed in the trilevel context and, as a result, efficient and … Read more