Generalized Nash equilibrium problems with mixed-integer variables constitute an important class of games in which each player solves a mixed-integer optimization problem, where both the objective and the feasible set is parameterized by the rivals’ strategies. However, such games are known for failing to admit exact equilibria and also the assumption of all players being … Read more
Many mathematical models base on the coupling of two or more optimization problems. This paper surveys possibilities to couple two optimization problems and discusses how solutions of the different models are interrelated with each other. The considered pairs stem from the fields of standard and generalized Nash equilibrium problems, optimistic and pessimistic bilevel problems, saddle … Read more
The rapid growth of online meal delivery has introduced complex logistical challenges, where platforms must dynamically assign orders to couriers while accounting for demand uncertainty, courier autonomy, and service efficiency. Traditional dispatching methods, often focused on short-term cost minimization, fail to capture the long-term implications of assignment decisions on system-wide performance. This paper presents a … Read more
Abstract One approach to solving optimal control problems is Bock’s direct multiple shoot- ing method. This method yields lifted nonlinear optimization problems (NLPs) with a spe- cific block structure. Exploiting this structure via tailored optimization algorithms can be computationally beneficial. We propose such methods, primarily within the framework of fil- ter line search sequential quadratic … Read more
Consider the context of solving a multi-objective stochastic optimization problem with one or more continuous objective functions to global optimality on a compact feasible set. For a simple algorithm that consists of selecting a finite set of feasible points using a space-filling design, expending the same number of simulation replications at each point to estimate … Read more
The variational inequality (VI) problem is a fundamental mathematical framework for many classical problems. This paper introduces an algorithm that applies to arbitrary finite-dimensional VIs with general compact convex sets and general continuous functions. The algorithm guarantees global linear convergence to an approximate solution without requiring any assumptions, including the typical monotonicity. Our approach adapts … Read more
The primary challenges in systemic risk measurement involve determining an overall reserve level of risk capital and allocating it to different components based on their systemic relevance. In this paper, we introduce a multivariate loss ratio measure (MLRM), which is the minimum amount of capital to be injected into a financial system such that the … Read more
A widely used approximation concept in multiobjective optimization is the concept of enclosures. These are unions of boxes defined by lower and upper bound sets that are used to cover optimal sets of multiobjective optimization problems in the image space. The width of an enclosure is taken as a quality measure. In this paper, we … Read more
Hypervolume is most likely the most often used set quality indicator in (evolutionary) multi-objective optimization. It may be used to compare the quality of solution sets whose images in the objective space are approximations of the true Pareto front. Although in this way we may compare two or more approximations, our knowledge is limited without … Read more
This paper introduces a generalized isotonic optimization framework over an arborescence graph, where each node incurs state-dependent convex costs and a fixed cost upon strict increases. We begin with the special case in which the arborescence is a path and develop a dynamic programming (DP) algorithm with an initial complexity of $O(n^3)$, which we improve … Read more