Other Topics

On Stationary Conditions and the Convergence of Augmented Lagrangian methods for Generalized Nash Equilibrium Problems

  • Lennin Mallma Ramirez
  • Frank Navarro Rojas
  • Alberto Ramos
    • Categories Constrained Nonlinear Optimization, Game Theory, Nonlinear Optimization Tags , , , ,

    In this work, we study stationarity conditions and constraint qualifications (CQs) tailored to Generalized Nash Equilibrium Problems (GNEPs) and analyze their relationships and implications for the global convergence of algorithms. We recall that GNEPs generalize Nash Equilibrium Problems (NEPs) in that the feasible strategy set of each player depends on the strategies chosen by the … Read more

    Solving Convex Quadratic Optimization with Indicators Over Structured Graphs

  • Aaresh Bhathena
  • Salar Fattahi
  • Andrés Gómez
  • Simge Küçükyavuz
    • Categories (Mixed) Integer Nonlinear Programming, Dynamic Programming Tags ,

    This paper studies convex quadratic minimization problems in which each continuous variable is coupled with a binary indicator variable. We focus on the structured setting where the Hessian matrix of the quadratic term is positive definite and exhibits sparsity. We develop an exact parametric dynamic programming algorithm whose computational complexity depends explicitly on the treewidth … Read more

    Dynamic and Robust Allocation of On-Street Parking for Passenger and Delivery Vehicles

  • Alp
  • Barış Yıldız
    • Categories Dynamic Programming, Robust Optimization, Transportation Tags , , , ,

    Problem definition: Curb space has long been a scarce public resource in automobilized cities, serving competing uses for passenger parking and commercial activities. The rapid growth of e-commerce and home deliveries, combined with increasing urban density, has further intensified pressure on this already constrained resource, making effective curbspace management a critical policy challenge. Yet, in … Read more

    Convergence Analysis of an Inertial Dynamical System with Hessian-Driven Damping under θ-Parametrized Implicit–Explicit Discretization

  • Milan Barik
  • Suvendu Ranjan Pattanaik
    • Categories Other Topics Tags

    In this paper, we consider an unconstrained composite convex optimisation problem. We propose an inertial forward–backward algorithm derived from an implicit– explicit discretisation of a second-order dynamical system with Hessian-driven damping. For α ≥ 3, we establish an O(1/d^2) convergence rate for the objective value gap. Furthermore, when α > 3, we prove that the … Read more

    Robust Admission Via Two-Stage Stable Matching Under Ranking Uncertainty

  • Gustavo Angulo
    • Categories Game Theory, Integer Programming, Robust Optimization Tags , , ,

    We study a two-stage admission and assignment problem under uncertainty arising in university admission systems. In the first stage, applicants are admitted to an initial two-year program. In the second stage, admitted applicants are assigned to degree programs through an articulation mechanism subject to capacity constraints. Uncertainty stems from the academic performance of admitted applicants … Read more

    A Surface-Based Formulation of the Traveling Salesman Problem

  • Yılmaz Arslanoğlu
    • Categories (Mixed) Integer Linear Programming, Other Topics Tags , , , ,

    We present an exact formulation of the symmetric Traveling Salesman Problem (TSP) that replaces the classical edge-selection view with a surface-building approach. Instead of selecting edges to form a cycle, the model selects a set of connected triangles where the boundary of the resulting surface forms the tour. This method yields a mixed-integer linear programming … Read more

    The colored knapsack problem: structural properties and exact algorithms

  • Fabio Ciccarelli
  • Alexander Helber
  • Erik Mühmer
    • Categories (Mixed) Integer Linear Programming, Combinatorial Optimization, Dynamic Programming Tags , , , ,

    We introduce and study a novel generalization of the classical Knapsack Problem (KP), called the Colored Knapsack Problem (CKP). In this problem, the items are partitioned into classes of colors and the packed items need to be ordered such that no consecutive items are of the same color. We establish that the problem is weakly … Read more

    Objective-Function Free Multi-Objective Optimization: Rate of Convergence and Performance of an Adagrad-like algorithm

  • Marianna De Santis
  • Gabriele Eichfelder
  • Margherita Porcelli
    • Categories Multi-Criteria Optimization, Unconstrained Optimization Tags , ,

    We propose an Adagrad-like algorithm for multi-objective unconstrained optimization that relies on the computation of a common descent direction only. Unlike classical local algorithms for multi-objective optimization, our approach does not rely on the dominance property to accept new iterates, which allows for a flexible and function-free optimization framework. New points are obtained using an … Read more

    An adaptive line-search-free multiobjective gradient method and its iteration-complexity analysis

  • Max L. N. Gonçalves
  • Geovani Nunes Grapiglia
  • Jefferson Gonçalves Melo
    • Categories Multi-Criteria Optimization, Unconstrained Optimization Tags , , ,

    This work introduces an Adaptive Line-Search-Free Multiobjective Gradient (AMG) method for solving smooth multiobjective optimization problems. The proposed approach automatically adjusts stepsizes based on steepest descent directions, promoting robustness with respect to stepsize choice while maintaining low computational cost. The method is specifically tailored to the multiobjective setting and does not rely on function evaluations, … Read more

    First-order Methods for Unconstrained Vector Optimization Problems: A Unified Majorization-Minimization Perspective

  • Jian Chen
    • Categories Multi-Criteria Optimization, Nonlinear Optimization, Stochastic Programming Tags , , , ,

    In this paper, we develop a unified majorization-minimization scheme and convergence analysis with first-order surrogate functions for unconstrained vector optimization problems (VOPs). By selecting different surrogate functions, the unified method can be reduced to various existing first-order methods. The unified convergence analysis reveals that the slow convergence of the steepest descent method is primarily attributed … Read more