Other Topics

On Supportedness-Promoting Image Space Transformations in Multiobjective Optimization

  • Felix Neussel
  • Oliver Stein
    • Categories Multi-Criteria Optimization Tags , , , ,

    We study the supportedness of nondominated points of multiobjective optimization problems, that is, whether they can be obtained via weighted sum scalarization. One key question is how supported points behave under an efficiency-preserving transformation of the original problem. Under a differentiability assumption, we characterize the transformations that preserve both efficiency and supportedness as the component-wise … Read more

    A One-Extra Player Reduction of GNEPs to NEPs

  • Henri Lefebvre
  • David Salas
  • Martin Schmidt
    • Categories Convex Optimization, Game Theory, Integer Programming Tags , , , ,

    It is common opinion that generalized Nash equilibrium problems are harder than Nash equilibrium problems. In this work, we show that by adding a new player, it is possible to reduce many generalized problems to standard equilibrium problems. The reduction holds for linear problems and smooth convex problems verifying a Slater-type condition. We also derive … Read more

    generalizing the successive shortest path algorithm to solve the multi-objective assignment problem

  • Antonio Sedeño-Noda
    • Categories Multi-Criteria Optimization, Network Optimization, Other Topics Tags , ,

    We introduce a novel characterization of the efficient solutions to the Multi-objective Assignment Problem (MAP), relying solely on Network Flow theory. This result establishes that the set of efficient assignments restricted to the first $k$ origin-destination pairs in the associated bipartite graph can be derived incrementally from the efficient solutions corresponding to the first $k-1$ … Read more

    Minimal Regret Walras Equilibria for Combinatorial Markets via Duality, Integrality, and Sensitivity Gaps

  • Alois Duguet
  • Tobias Harks
  • Martin Schmidt
  • Julian Schwarz
    • Categories Game Theory Tags , , , , ,

    We consider combinatorial multi-item markets and propose the notion of a ∆-regret Walras equilibrium, which is an allocation of items to players and a set of item prices that achieve the following goals: prices clear the market, the allocation is capacity-feasible, and the players’ strategies lead to a total regret of ∆. The regret is … Read more

    Branch-and-Cut for Computing Approximate Equilibria of Mixed-Integer Generalized Nash Games

  • Alois Duguet
  • Tobias Harks
  • Martin Schmidt
  • Julian Schwarz
    • Categories (Mixed) Integer Nonlinear Programming, Branch and Cut Algorithms, Game Theory Tags , , , ,

    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

    A guided tour through the zoo of paired optimization problems

  • Oliver Stein
    • Categories Bilevel Optimization, Game Theory, Nonlinear Optimization Tags , , , , , , , , ,

    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

    Data-Driven Optimization for Meal Delivery: A Reinforcement Learning Approach for Order-Courier Assignment and Routing at Meituan

  • Ramon Auad
  • Felipe Lagos
  • Tomas Lagos
    • Categories Dynamic Programming, Meta Heuristics, Transportation Tags

    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

    blockSQP 2: exploiting structure to improve performance

  • Reinhold Wittmann
  • Sebastian Sager
    • Categories Dynamic Programming, Nonlinear Optimization Tags , , , ,

    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

    Global Multi-Objective Simulation Optimization: Error Bounds and Convergence Rates

  • Burla E. Ondes
  • Susan R. Hunter
    • Categories Global Optimization, Multi-Criteria Optimization, Optimization of Simulated Systems Tags , , , ,

    Consider the context of solving a multi-objective simulation 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

    A linearly convergent algorithm for variational inequalities based on fiber bundle

  • Hongbo Sun
    • Categories Complementarity and Variational Inequalities, Game Theory Tags , , ,

    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