Accelerating Domain Propagation: an Efficient GPU-Parallel Algorithm over Sparse Matrices

  • Ambros Gleixner
  • Sebastian Pokutta
  • Boro Sofranac
    • Categories Integer Programming Tags , , , ,

    Fast domain propagation of linear constraints has become a crucial component of today’s best algorithms and solvers for mixed integer programming and pseudo-boolean optimization to achieve peak solving performance. Irregularities in the form of dynamic algorithmic behaviour, dependency structures, and sparsity patterns in the input data make efficient implementations of domain propagation on GPUs and, … Read more

    Spectral Residual Method for Nonlinear Equations on Riemannian Manifolds

  • Hugo Lara
  • Harry Oviedo
    • Categories Nonlinear Systems and Least-Squares Tags , , , ,

    In this paper, the spectral algorithm for nonlinear equations (SANE) is adapted to the problem of finding a zero of a given tangent vector field on a Riemannian manifold. The generalized version of SANE uses, in a systematic way, the tangent vector field as a search direction and a continuous real–valued function that adapts this … Read more

    Regret Minimization in Stochastic Non-Convex Learning via a Proximal-Gradient Approach

  • Volkan Cevher
  • Nadav Hallak
  • Panayotis Mertikopoulos
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization

    Motivated by applications in machine learning and operations research, we study regret minimization with stochastic first-order oracle feedback in online constrained, and possibly non-smooth, non-convex problems. In this setting, the minimization of external regret is beyond reach, so we focus on a local regret measures defined via a proximal-gradient residual mapping. To achieve no (local) … Read more

    Using first-order information in Direct Multisearch for multiobjective optimization

  • Roberto Andreani
  • Ana Luisa Custódio
  • Marcos Raydan
    • Categories Bound-constrained Optimization, Multi-Criteria Optimization, Nonlinear Optimization Tags , , , ,

    Derivatives are an important tool for single-objective optimization. In fact, it is commonly accepted that derivative-based methods present a better performance than derivative-free optimization approaches. In this work, we will show that the same does not apply to multiobjective derivative-based optimization, when the goal is to compute an approximation to the complete Pareto front of … Read more

    Constrained global optimization of functions with low effective dimensionality using multiple random embeddings

  • Coralia Cartis
  • Estelle Massart
  • Adilet Otemissov
    • Categories Global Optimization, Nonlinear Optimization Tags , , ,

    We consider the bound-constrained global optimization of functions with low effective dimensionality, that are constant along an (unknown) linear subspace and only vary over the effective (complement) subspace. We aim to implicitly explore the intrinsic low dimensionality of the constrained landscape using feasible random embeddings, in order to understand and improve the scalability of algorithms … Read more

    Economic inexact restoration for derivative-free expensive function minimization and applications

  • Ernesto G. Birgin
  • Nataša Krejić
  • José Mario Martínez
    • Categories Nonlinear Optimization Tags , , , ,

    The Inexact Restoration approach has proved to be an adequate tool for handling the problem of minimizing an expensive function within an arbitrary feasible set by using different degrees of precision in the objective function. The Inexact Restoration framework allows one to obtain suitable convergence and complexity results for an approach that rationally combines low- … Read more

    A Branch-Cut-and-Price Algorithm for the Time-Dependent Electric Vehicle Routing Problem with Time Windows

  • Gonzalo Lera-Romero
  • Juan José Miranda-Bront
  • Francisco J. Soulignac
    • Categories Applications - OR and Management Sciences, Combinatorial Optimization

    The adoption of electric vehicles (EVs) within last-mile deliveries is considered one of the key transformations towards more sustainable logistics. The inclusion of EVs introduces new operational constraints to the models such as a restricted driving range and the possibility to perform recharges in-route. The discharge of the typical batteries is complex and depends on … Read more

    Adaptable Energy Management System for Smart Buildings

  • Miguel F. Anjos
  • Juan A. Gomez-Herrera
  • Kenneth McKinnon
  • Ilaria Salerno
    • Categories Applications - OR and Management Sciences, Civil and Environmental Engineering, Optimization of Simulated Systems Tags , , , ,

    This paper presents a novel adaptable energy management system for smart buildings. In this framework we model the energy consumption of a living unit, and its energy exchange with the surroundings. We explicitly consider the impact of the outside environment and design features such as building orientation, automatic shading, and double facade. We formulate this … Read more

    Inexact Variable Metric Method for Convex-Constrained Optimization Problems

  • Douglas S. Gonçalves
  • Max L. N. Gonçalves
  • Tiago Menezes
    • Categories Constrained Nonlinear Optimization

    This paper is concerned with the inexact variable metric method for solving convex-constrained optimization problems. At each iteration of this method, the search direction is obtained by inexactly minimizing a strictly convex quadratic function over the closed convex feasible set. Here, we propose a new inexactness criterion for the search direction subproblems. Under mild assumptions, … Read more

    Largest small polygons: A sequential convex optimization approach

  • Christian Bingane
    • Categories Constrained Nonlinear Optimization, Convex Optimization, Quadratic Programming Tags , , , , ,

    A small polygon is a polygon of unit diameter. The maximal area of a small polygon with $n=2m$ vertices is not known when $m\ge 7$. Finding the largest small $n$-gon for a given number $n\ge 3$ can be formulated as a nonconvex quadratically constrained quadratic optimization problem. We propose to solve this problem with a … Read more