A Subspace Minimization Barzilai-Borwein Method for Multiobjective Optimization Problems

  • Jian Chen
    • Categories Multi-Criteria Optimization Tags , , ,

    Nonlinear conjugate gradient methods have recently garnered significant attention within the multiobjective optimization community. These methods aim to maintain consistency in conjugate parameters with their single-objective optimization counterparts. However, the preservation of the attractive conjugate property of search directions remains uncertain, even for quadratic cases, in multiobjective conjugate gradient methods. This loss of interpretability of … Read more

    The Bipartite Implication Polytope: Conditional Relations over Multiple Sets of Binary Variables

  • Robert Burlacu
  • Patrick Gemander
  • Tobias Kuen
    • Categories 0-1 Programming, Polyhedra, Quadratic Programming Tags , , , , , , , ,

    Inspired by its occurrence as a substructure in a stochastic railway timetabling model, we study in this work a special case of the bipartite boolean quadric polytope. It models conditional relations across three sets of binary variables, where selections within two implying sets imply a choice in a corresponding implied set. We call this polytope … Read more

    The Multi-Stop Station Location Problem: Exact Approaches

  • Erik Mühmer
  • Miriam Ganz
  • Marco E. Lübbecke
  • Felix J. L. Willamowski
    • Categories (Mixed) Integer Linear Programming, Branch and Cut Algorithms, Transportation Tags , ,

    The multi-stop station location problem (MSLP) aims to place stations such that a set of trips is feasible with respect to length bounds while minimizing cost. Each trip consists of a sequence of stops that must be visited in a given order, and a length bound that controls the maximum length that is possible without … Read more

    New cuts and a branch-cut-and-price model for the Multi Vehicle Covering Tour Problem

  • Bruno Oliveira
  • Artur Alves Pessoa
  • Marcos Roboredo
    • Categories Combinatorial Optimization, Cutting Plane Approaches, Integer Programming Tags , , , ,

    The Multi-Vehicle Covering Tour Problem (m-CTP) involves a graph in which the set of vertices is partitioned into a depot and three distinct subsets representing customers, mandatory facilities, and optional facilities. Each customer is linked to a specific subset of optional facilities that define its coverage set. The goal is to determine a set of … Read more

    A Clustering-based uncertainty set for Robust Optimization

  • Alireza Yazdani
  • Ahmadreza Marandi
  • Rob Basten
  • Lijia Tan
    • Categories (Mixed) Integer Nonlinear Programming, Cone Programming, Robust Optimization Tags , , , , ,

    Robust optimization is an approach for handling uncertainty in optimization problems, in which the uncertainty set determines the conservativeness of the solutions. In this paper, we propose a data-driven uncertainty set using a type of volume-based clustering, which we call Minimum-Volume Norm-Based Clustering (MVNBC). MVNBC extends the concept of minimum-volume ellipsoid clustering by allowing clusters … Read more

    Heuristic Methods for Γ-Robust Mixed-Integer Linear Bilevel Problems

  • Yasmine Beck
  • Ivana Ljubić
  • Martin Schmidt
    • Categories (Mixed) Integer Linear Programming, Robust Optimization Tags , , ,

    Due to their nested structure, bilevel problems are intrinsically hard to solve–even if all variables are continuous and all parameters of the problem are exactly known. In this paper, we study mixed-integer linear bilevel problems with lower-level objective uncertainty, which we address using the notion of Γ-robustness. To tackle the Γ-robust counterpart of the bilevel … Read more

    A Parametric Approach for Solving Convex Quadratic Optimization with Indicators Over Trees

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

    This paper investigates convex quadratic optimization problems involving $n$ indicator variables, each associated with a continuous variable, particularly focusing on scenarios where the matrix $Q$ defining the quadratic term is positive definite and its sparsity pattern corresponds to the adjacency matrix of a tree graph. We introduce a graph-based dynamic programming algorithm that solves this … Read more

    A Proximal-Gradient Method for Constrained Optimization

  • Daniel P. Robinson
  • Yutong Dai
  • Xiaoyi Qu
    • Categories Nonlinear Optimization, Optimization in Data Science Tags , , , , ,

    We present a new algorithm for solving optimization problems with objective functions that are the sum of a smooth function and a (potentially) nonsmooth regularization function, and nonlinear equality constraints. The algorithm may be viewed as an extension of the well-known proximal-gradient method that is applicable when constraints are not present. To account for nonlinear … Read more

    A Bilevel Hierarchy of Strengthened Complex Moment Relaxations for Complex Polynomial Optimization

  • Jie Wang
    • Categories Constrained Nonlinear Optimization, Global Optimization Theory, Semi-definite Programming Tags , , ,

    This paper proposes a bilevel hierarchy of strengthened complex moment relaxations for complex polynomial optimization. The key trick entails considering a class of positive semidefinite conditions that arise naturally in characterizing the normality of the so-called shift operators. The relaxation problem in this new hierarchy is parameterized by the usual relaxation order as well as … Read more