Month: March 2023

An Explicit Three-Term Polak-Ribière-Polyak Conjugate Gradient Method for Bicriteria Optimization

  • Mounir El Maghri
  • Youssef Elboulqe
    • Categories Multi-Criteria Optimization, Unconstrained Optimization Tags , , , , ,

    We propose in this paper a Polak-Ribière-Polyak conjugate gradient type method for solving bicriteria optimization problems by avoiding scalarization techniques. Two particular advantages in this contribution are to be noted. First, the suggested descent direction common to both criteria may be directly computed by a given formula without solving any intermediate subproblem. Second, the descent … Read more

    Mixed-Integer Quadratic Optimization and Iterative Clustering Techniques for Semi-Supervised Support Vector Machines

  • Martin Schmidt
  • Jan Pablo Burgard
  • Maria Eduarda Pinheiro
    • Categories (Mixed) Integer Nonlinear Programming, Data Science Algorithms, Data Science Applications Tags , , ,

    Among the most famous algorithms for solving classification problems are support vector machines (SVMs), which find a separating hyperplane for a set of labeled data points. In some applications, however, labels are only available for a subset of points. Furthermore, this subset can be non-representative, e.g., due to self-selection in a survey. Semi-supervised SVMs tackle … Read more

    Safe and Verified Gomory Mixed Integer Cuts in a Rational MIP Framework

  • Leon Eifler
  • Ambros Gleixner
    • Categories (Mixed) Integer Linear Programming Tags , , ,

    This paper is concerned with the exact solution of mixed-integer programs (MIPs) over the rational numbers, i.e., without any roundoff errors and error tolerances. Here, one computational bottleneck that should be avoided whenever possible is to employ large-scale symbolic computations. Instead it is often possible to use safe directed rounding methods, e.g., to generate provably … Read more

    Solving low-rank semidefinite programs via manifold optimization

  • Jie Wang
    • Categories Constrained Nonlinear Optimization, Optimization Software Benchmark, Semi-definite Programming Tags , , , , ,

    We propose a manifold optimization approach to solve linear semidefinite programs (SDP) with low-rank solutions. This approach incorporates the augmented Lagrangian method and the Burer-Monteiro factorization, and features the adaptive strategies for updating the factorization size and the penalty parameter. We prove that the present algorithm can solve SDPs to global optimality, despite of the … Read more

    A Stochastic Benders Decomposition Scheme for Large-Scale Stochastic Network Design

  • Dimitris Bertsimas
  • Ryan Cory-Wright
  • Jean Pauphilet
  • Periklis Petridis
    • Categories Cutting Plane Approaches, Network Optimization, Stochastic Programming Tags , ,

    Network design problems involve constructing edges in a transportation or supply chain network to minimize construction and daily operational costs. We study a stochastic version where operational costs are uncertain due to fluctuating demand and estimated as a sample average from historical data. This problem is computationally challenging, and instances with as few as  100 … Read more

    On a Frank-Wolfe Approach for Abs-smooth Functions

  • Timo Kreimeier
  • Sebastian Pokutta
  • Andrea Walther
  • Zev Woodstock
    • Categories Constrained Nonlinear Optimization, Nonsmooth Optimization, Other Topics Tags , , , ,

    We propose an algorithm which appears to be the first bridge between the fields of conditional gradient methods and abs-smooth optimization. Our problem setting is motivated by various applications that lead to nonsmoothness, such as $\ell_1$ regularization, phase retrieval problems, or ReLU activation in machine learning. To handle the nonsmoothness in our problem, we propose … Read more

    Effective matrix adaptation strategy for noisy derivative-free optimization

  • Morteza Kimiaei
  • Arnold Neumaier
    • Categories Global Optimization Applications, Nonlinear Optimization, Optimization Software Benchmark Tags

    In this paper, we introduce a new effective matrix adaptation evolution strategy (MADFO) for noisy derivative-free optimization problems. Like every MAES solver, MADFO consists of three phases: mutation, selection and recombination. MADFO improves the mutation phase by generating good step sizes, neither too small nor too large, that increase the probability of selecting mutation points … Read more

    Cooperative locker locations games

  • Fabio Mercurio
  • Loe Schlicher
  • S.U.K Rohmer
  • Tom Van Woensel
    • Categories Applications - OR and Management Sciences, Game Theory, Other Topics Tags , ,

    More and more people are ordering products online, having their parcels delivered to their homes. This leads to more congestion, which negatively impacts the environment as well as public health and safety. To reduce these negative impacts, carriers can use parcel lockers to consolidate and serve their customers. The implementation of a locker network can, … Read more

    An approximation algorithm for multi-objective mixed-integer convex optimization

  • Ina Lammel
  • Karl-Heinz Küfer
  • Philipp Süss
    • Categories (Mixed) Integer Nonlinear Programming, Multi-Criteria Optimization Tags , ,

    In this article we introduce an algorithm that approximates Pareto fronts of multiobjective mixed-integer convex optimization problems. The algorithm constructs an inner and outer approximation of the front exploiting the convexity of the patches and is applicable to problems with an arbitrary number of criteria. In the algorithm, the problem is decomposed into patches, which … Read more

    Stable Set Polytopes with High Lift-and-Project Ranks for the Lovász-Schrijver SDP Operator

  • Yu Hin (Gary) Au
  • Levent Tunçel
    • Categories Combinatorial Optimization, Cutting Plane Approaches, Semi-definite Programming Tags , , , ,

    We study the lift-and-project rank of the stable set polytopes of graphs with respect to the Lovász-Schrijver SDP operator \( \text{LS}_+\), with a particular focus on a search for relatively small graphs with high \( \text{LS}_+\)-rank (the least number of iterations of the \( \text{LS}_+\) operator on the fractional stable set polytope to compute the … Read more