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Stochastic block coordinate and function alternation for multi-objective optimization and learning

  • Trang H. Tran
  • Luis Nunes Vicente
    • Categories Multi-Criteria Optimization Tags , , ,

    Multi-objective optimization is central to many engineering and machine learning applications, where multiple objectives must be optimized in balance. While multi-gradient based optimization methods combine these objectives in each step, such methods require computing gradients with respect to all variables at every iteration, resulting in high computational costs in large-scale settings. In this work, we … Read more

    A Binary Search-Based Criterion Space Algorithm for Solving Bi-Objective Integer Programs: The Quadtree Search Method

  • Lagnajita Basu
  • Aadya Bhattarai
  • Tapas Das
  • Kimia Keshanian
  • Hadi Charkhgard
    • Categories Integer Programming, Multi-Criteria Optimization Tags , , , ,

    We propose an exact binary search-based branch-and-bound algorithm, termed the Quadtree Search Method, for solving bi-objective integer programs. The existing literature on criterion space search methods for multi-objective optimization predominantly assumes that subproblems can be solved to optimality, an assumption that becomes computationally prohibitive for hard instances. In contrast, our approach departs from this assumption … Read more

    Supervised feature selection via multiobjective programming and its application in the medical field

  • Pham Thi Hoai
    • Categories Applications - OR and Management Sciences, Constrained Nonlinear Optimization, Convex and Nonsmooth Optimization, Convex Optimization, Other Topics Tags , , , ,

    In this study, we model the supervised feature selection problem using a novel approach: convex bi-objective optimization. Traditional methods have addressed this problem by maximizing relevance to class labels and minimizing redundancy among features. Recently, Wang et al. [30] formulated this problem as a single-objective convex optimization, yielding only a unique solution. Unlike that, we … Read more

    Paving and computing the set of nondominated points for the bi-objective 0/1 uncapacitated facility location problem

  • Xavier Gandibleux
  • Anthony Przybylski
    • Categories Combinatorial Optimization, Multi-Criteria Optimization Tags , , , , ,

    The paper presents a three-phase algorithm to compute the set of nondominated points for the binary version of the uncapacitated facility location problem with two objectives. The first phase constructs a paving in objective space which is a collection of boxes that covers all nondominated points. The paving procedure is a branch and bound algorithm … Read more

    An Interpretable Ensemble Heuristic for Principal-Agent Games with Machine Learning

  • I. Esra Buyuktahtakin Toy
    • Categories Applications - OR and Management Sciences, Game Theory, Optimization in Data Science

    This paper addresses the challenge of enhancing public policy decision-making by efficiently solving principal-agent models (PAMs) for public-private partnerships, a critical yet computationally demanding problem. We develop a fast, interpretable, and generalizable approach to support policy decisions under these settings. We propose an interpretable ensemble heuristic (EH) that integrates Machine Learning (ML), Operations Research (OR), … Read more

    Optimal Transport on Lie Group Orbits

  • Bahar Taskesen
    • Categories Infinite Dimensional Optimization, Other Topics

    In its most general form, the optimal transport problem is an infinite-dimensional optimization problem, yet certain notable instances admit closed-form solutions. We identify the common source of this tractability as symmetry and formalize it using Lie group theory. Fixing a Lie group action on the outcome space and a reference distribution, we study optimal transport … Read more

    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

    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