Recursive Partitioning and Batching for Network Design with Service Time Guarantees at Massive Scale

  • Myungeun Eom
  • Alan L. Erera
  • Alejandro Toriello
    • Categories Production and Logistics, Supply Chain Management, Transportation Tags , , , ,

    Motivated by the parcel delivery industry, we study a network design problem with service time guarantees at industrial scale. This tactical service network design problem determines primary paths and delivery schedules for commodities to minimize transportation and handling costs while ensuring committed service times. To construct a solution for a real-world instance with over 1,000 … Read more

    Tight Semidefinite Relaxations for Verifying Robustness of Neural Networks

  • Godai Azuma
  • Sunyoung Kim
  • Makoto Yamashita
    • Categories Optimization in Data Science, Quadratic Programming, Semi-definite Programming Tags , , , ,

    For verifying the safety of neural networks (NNs), Fazlyab et al. (2019) introduced a semidefinite programming (SDP) approach called DeepSDP. This formulation can be viewed as the dual of the SDP relaxation for a problem formulated as a quadratically constrained quadratic program (QCQP). While SDP relaxations of QCQPs generally provide approximate solutions with some gaps, … Read more

    A relaxed version of Ryu’s three-operator splitting method for structured nonconvex optimization

  • Felipe Atenas
  • Jan Harold Alcantara
    • Categories Nonlinear Optimization, Nonsmooth Optimization

    In this work, we propose a modification of Ryu’s splitting algorithm for minimizing the sum of three functions, where two of them are convex with Lipschitz continuous gradients, and the third is an arbitrary proper closed function that is not necessarily convex. The modification is essential to facilitate the convergence analysis, particularly in establishing a … Read more

    Rounding the Lovasz Theta Function with a Value Function Approximation

  • Rui Gong
  • Diego Cifuentes
  • Alejandro Toriello
    • Categories Dynamic Programming, Graphs and Matroids, Semi-definite Programming Tags , , , ,

    The Lovasz theta function is a semidefinite programming (SDP) relaxation for the maximum weighted stable set problem, which is tight for perfect graphs. However, even for perfect graphs, there is no known rounding method guaranteed to extract an optimal stable set from the SDP solution. In this paper, we develop a novel rounding scheme for … Read more

    An iterative process for the feasibility-seeking problem with sets that are unions of convex sets

  • Yair Censor
  • Alexander J. Zaslavski
    • Categories Constrained Nonlinear Optimization, Convex Optimization Tags , , , ,

    In this paper we deal with the feasibility-seeking problem for unions of convex sets (UCS) sets and propose an iterative process for its solution. Renewed interest in this problem stems from the fact that it was recently discovered to serve as a modeling approach in fields of applications and from the ongoing recent research efforts … Read more

    Direct-search methods for decentralized blackbox optimization

  • Elhoucine Bergou
  • Youssef Diouane
  • Vyacheslav Kungurtsev
  • Clément W. Royer
    • Categories Network Optimization, Nonlinear Optimization, Unconstrained Optimization

    Derivative-free optimization algorithms are particularly useful for tackling blackbox optimization problems where the objective function arises from complex and expensive procedures that preclude the use of classical gradient-based methods. In contemporary decentralized environments, such functions are defined locally on different computational nodes due to technical or privacy constraints, introducing additional challenges within the optimization process. … Read more

    On the Semidefinite Representability of Continuous Quadratic Submodular Minimization With Applications to Moment Problems

  • Samuel Burer
  • Karthik Natarajan
    • Categories Quadratic Programming, Robust Optimization, Semi-definite Programming Tags , ,

    We study continuous quadratic submodular minimization with bounds and propose a polynomially sized semidefinite relaxation, which is provably tight for dimension n ≤ 3 and empirically tight for larger n. We apply the relaxation to two moment problems arising in distributionally robust optimization and the computation of covariance bounds. Accordingly, this research advances the ongoing … Read more

    On regularized structure exploiting Quasi-Newton methods for inverse problems

  • Raphael Kuess
  • Andrea Walther
    • Categories Infinite Dimensional Optimization, Nonlinear Systems and Least-Squares Tags , , , ,

    This paper introduces a regularized, structure-exploiting Powell-Symmetric-Broyden (RSE-PSB) method under modified secant conditions for solving ill-posed inverse problems in both infinite dimensional and finite dimensional settings. The approximation of the symmetric, yet potentially indefinite, second-order term, which is neglected by standard Levenberg-Marquardt (LM) approaches, integrates regularization and structure exploitation directly within the Quasi-Newton (QN) framework, … Read more

    Extending Exact Convex Relaxations of Quadratically Constrained Quadratic Programs

  • Masakazu Kojima
  • Sunyoung Kim
  • Naohiko Arima
    • Categories Convex Optimization, Global Optimization, Semi-definite Programming Tags , , , ,

    A convex relaxation of a quadratically constrained quadratic program (QCQP) is called exact if it has a rank-$1$ optimal solution that corresponds to an optimal solution of the  QCQP. Given a QCQP whose convex relaxation is exact,  this paper investigates the incorporation of additional quadratic inequality constraints under a non-intersecting quadratic constraint condition while maintaining … Read more

    Efficient search strategies for constrained multiobjective blackbox optimization

  • Sébastien Le Digabel
  • Antoine Lesage-Landry
  • Ludovic Salomon
  • Christophe Tribes
    • Categories Multi-Criteria Optimization, Nonlinear Optimization Tags ,

    Multiobjective blackbox optimization deals with problems where the objective and constraint functions are the outputs of a numerical simulation. In this context, no derivatives are available, nor can they be approximated by finite differences, which precludes the use of classical gradient-based techniques. The DMulti-MADS algorithm implements a state-of-the-art direct search procedure for multiobjective blackbox optimization … Read more