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
We develop and analyze an inexact regularized alternating projection method for nonconvex feasibility problems. Such a method employs inexact projections on one of the two sets, according to a set of well-defined conditions. We prove the global convergence of the algorithm, provided that a certain merit function satisfies the Kurdyka-Lojasiewicz property on its domain. The … Read more
We propose new adaptive strategies to compute stepsizes for the steepest descent method to solve unconstrained nonlinear multiobjective optimization problems without employing any linesearch procedure. The resulting algorithms can be applied to a wide class of nonconvex unconstrained multi-criteria optimization problems satisfying a global Lipschitz continuity condition imposed on the gradients of all objectives. In … Read more
Since the inception of ISOs, Locational Marginal Prices (LMPs) alone were not market clearing or incentive compatible because an auction winner who offered its avoidable costs could lose money at the LMPs. ISOs used make-whole payments to ensure that market participants did not lose money. Make-whole payments were not public, creating transparency issues. Over time, … Read more
Multiobjective binary quadratic programming refers to optimization problems involving multiple quadratic – potentially non-convex – objective functions and a feasible set that includes binary constraints on the variables. In this paper, we extend the well-established Quadratic Convex Reformulation technique, originally developed for single-objective binary quadratic programs, to the multiobjective setting. We propose a branch-and-bound algorithm … Read more
This paper considers monotone transformations of the objective space of multiobjective optimization problems which leave the set of efficient points invariant. Under mild assumptions, for the standard ordering cone we show that such transformations must be component-wise transformations. The same class of transformations also leaves the sets of weakly and of Geoffrion properly efficient points … Read more