Optimization Software and Modeling Systems

Exploiting Low-Rank Structure in Semidefinite Programming by Approximate Operator Splitting

  • Joaquim Dias Garcia
  • Mario Souto
  • Alvaro Viega
    • Categories Convex Optimization, Optimization Software and Modeling Systems, Semi-definite Programming Tags , , , , ,

    In contrast with many other convex optimization classes, state-of-the-art semidefinite programming solvers are yet unable to efficiently solve large scale instances. This work aims to reduce this scalability gap by proposing a novel proximal algorithm for solving general semidefinite programming problems. The proposed methodology, based on the primal-dual hybrid gradient method, allows the presence of … Read more

    POLO: a POLicy-based Optimization library

  • Arda Aytekin
  • Martin Biel
  • Mikael Johansson
    • Categories Convex and Nonsmooth Optimization, Optimization Software Design Principles, Parallel Algorithms Tags , , , ,

    We present POLO — a C++ library for large-scale parallel optimization research that emphasizes ease-of-use, flexibility and efficiency in algorithm design. It uses multiple inheritance and template programming to decompose algorithms into essential policies and facilitate code reuse. With its clear separation between algorithm and execution policies, it provides researchers with a simple and powerful … Read more

    Parallelizable Algorithms for Optimization Problems with Orthogonality Constraints

  • Bin Gao
  • Xin Liu
  • Ya-xiang Yuan
    • Categories Constrained Nonlinear Optimization, Parallel Algorithms

    To construct a parallel approach for solving optimization problems with orthogonality constraints is usually regarded as an extremely difficult mission, due to the low scalability of the orthonormalization procedure. However, such demand is particularly huge in some application areas such as materials computation. In this paper, we propose a proximal linearized augmented Lagrangian algorithm (PLAM) … Read more

    Rapid prototyping of parallel primal heuristics for domain specific MIPs: Application to maritime inventory routing

  • Shabbir Ahmed
  • Lluís-Miquel Munguía
  • George L. Nemhauser
  • Dimitri J. Papageorgiou
  • David A. Bader
  • Yufen Shao
    • Categories (Mixed) Integer Linear Programming, Parallel Algorithms, Transportation

    Parallel Alternating Criteria Search (PACS) relies on the combination of computer parallelism and Large Neighborhood Searches to attempt to deliver high quality solutions to any generic Mixed-Integer Program (MIP) quickly. While general-purpose primal heuristics are widely used due to their universal application, they are usually outperformed by domain-specific heuristics when optimizing a particular problem class. … Read more

    Outer Approximation With Conic Certificates For Mixed-Integer Convex Problems

  • Chris Coey
  • Miles Lubin
  • Juan Pablo Vielma
    • Categories (Mixed) Integer Nonlinear Programming, Linear, Cone and Semidefinite Programming, Optimization Software Benchmark Tags , ,

    A mixed-integer convex (MI-convex) optimization problem is one that becomes convex when all integrality constraints are relaxed. We present a branch-and-bound LP outer approximation algorithm for an MI-convex problem transformed to MI-conic form. The polyhedral relaxations are refined with K* cuts} derived from conic certificates for continuous primal-dual conic subproblems. Under the assumption that all … Read more

    Minimizing convex quadratics with variable precision Krylov methods

  • Serge Gratton
  • Philippe L. Toint
  • Ehouarn Simon
    • Categories Convex Optimization, Optimization Software and Modeling Systems, Quadratic Programming Tags , ,

    Iterative algorithms for the solution of convex quadratic optimization problems are investigated, which exploit inaccurate matrix-vector products. Theoretical bounds on the performance of a Conjugate Gradients and a Full-Orthormalization methods are derived, the necessary quantities occurring in the theoretical bounds estimated and new practical algorithms derived. Numerical experiments suggest that the new methods have significant … Read more

    Decentralized Algorithms for Distributed Integer Programming Problems with a Coupling Cardinality Constraint

  • Shabbir Ahmed
  • George L. Nemhauser
  • Ezgi Karabulut
    • Categories 0-1 Programming, Parallel Algorithms Tags , ,

    We consider a multi-player optimization where each player has her own optimization problem and the individual problems are connected by a cardinality constraint on their shared resources. We give distributed algorithms that allow each player to solve their own optimization problem and still achieve a global optimization solution for problems that possess a concavity property. … Read more

    The Supporting Hyperplane Optimization Toolkit

  • Jan Kronqvist
  • Andreas Lundell
  • Tapio Westerlund
    • Categories (Mixed) Integer Nonlinear Programming, Optimization Software and Modeling Systems Tags , , , , ,

    In this paper, an open source solver for mixed-integer nonlinear programming (MINLP) problems is presented. The Supporting Hyperplane Optimization Toolkit (SHOT) combines a dual strategy based on polyhedral outer approximations (POA) with primal heuristics. The outer approximation is achieved by expressing the nonlinear feasible set of the MINLP problem with linearizations obtained with the extended … Read more

    Selection of variables in parallel space decomposition for the mesh adaptive direct search algorithm

  • Stéphane Alarie
  • Nadir Amaioua
  • Charles Audet
  • Sébastien Le Digabel
  • Louis-Alexandre Leclaire
    • Categories Nonlinear Optimization, Parallel Algorithms

    The parallel space decomposition of the Mesh Adaptive Direct Search algorithm (PSDMADS proposed in 2008) is an asynchronous parallel method for constrained derivative-free optimization with large number of variables. It uses a simple generic strategy to decompose a problem into smaller dimension subproblems. The present work explores new strategies for selecting subset of variables defining … Read more

    A Review and Comparison of Solvers for Convex MINLP

  • David E. Bernal Neira
  • Ignacio E. Grossmann
  • Andreas Lundell
  • Jan Kronqvist
    • Categories (Mixed) Integer Nonlinear Programming, Optimization Software Benchmark

    In this paper, we present a review of deterministic software for solving convex MINLP problems as well as a comprehensive comparison of a large selection of commonly available solvers. As a test set, we have used all MINLP instances classified as convex in the problem library MINLPLib, resulting in a test set of 366 convex … Read more