Optimization Software Benchmark

A Comparison of Nonsmooth, Nonconvex, Constrained Optimization Solvers for the Design of Time-Delay Compensators

  • Vyacheslav Kungurtsev
  • Tim Mitchell
  • Tomas Vyhlidal
    • Categories Control Applications, Nonsmooth Optimization, Optimization Software Benchmark

    We present a detailed set of performance comparisons of two state-of-the-art solvers for the application of designing time-delay compensators, an important problem in the field of robust control. Formulating such robust control mechanics as constrained optimization problems often involves objective and constraint functions that are both nonconvex and nonsmooth, both of which present significant challenges … Read more

    Largest Small n-Polygons: Numerical Results and Conjectured Optima

  • János Pintér
    • Categories Global Optimization Applications, Modeling Languages and Systems, Optimization Software Benchmark Tags , , , , , ,

    LSP(n), the largest small polygon with n vertices, is defined as the polygon of unit diameter that has maximal area A(n). Finding the configuration LSP(n) and the corresponding A(n) for even values n >= 6 is a long-standing challenge that leads to an interesting class of nonlinear optimization problems. We present numerical solution estimates for … 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

    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

    A computational study of global optimization solvers on two trust region subproblems

  • Ferenc Domes
  • Arnold Neumaier
  • Tiago Montanher
    • Categories Global Optimization, Global Optimization Applications, Optimization Software Benchmark

    One of the relevant research topics to which Chris Floudas contributed was quadratically constrained quadratic programming (QCQP). This paper considers one of the simplest hard cases of QCQP, the two trust region subproblem (TTRS). In this case, one needs to minimize a quadratic function constrained by the intersection of two ellipsoids. The Lagrangian dual of … Read more

    A note on using performance and data profiles for training algorithms

  • Margherita Porcelli
  • Philippe L. Toint
    • Categories Nonlinear Optimization, Optimization of Simulated Systems, Optimization Software Benchmark Tags , , ,

    It is shown how to use the performance and data profile benchmarking tools to improve algorithms’ performance. An illustration for the BFO derivative-free optimizer suggests that the obtained gains are potentially significant. Citation ACM Transactions on Mathematical Software, 45:2 (2019), Article 20. Article Download View A note on using performance and data profiles for training … Read more

    BASBL: Branch-And-Sandwich BiLevel solver. II. Implementation and computational study with the BASBLib test set

  • Claire S. Adjiman
  • Polyxeni-Margarita Kleniati
  • Remigijus Paulavicius
    • Categories Global Optimization Applications, Optimization Software Benchmark Tags , , , , ,

    We describe BASBL, our implementation of the deterministic global optimization algorithm Branch-and-Sandwich for nonconvex/nonlinear bilevel problems, within the open-source MINOTAUR framework. The solver incorporates the original Branch-and-Sandwich algorithm and modifications proposed in the first part of this work. We also introduce BASBLib, an extensive online library of bilevel benchmark problems collected from the literature and … Read more

    On the effectiveness of primal and dual heuristics for the transportation problem

  • Jonas Schwinn
  • Ralf Werner
    • Categories Linear Programming, Optimization Software Benchmark

    The transportation problem is one of the most popular problems in linear programming. Over the course of time a multitude of exact solution methods and heuristics have been proposed. Due to substantial progress of exact solvers since the mid of the last century, the interest in heuristics for the transportation problem over the last few … Read more

    A simple preprocessing algorithm for semidefinite programming

  • Preston Faulk
  • Gabor Pataki
  • Quoc Tran-Dinh
    • Categories Convex Optimization, Optimization Software Benchmark, Semi-definite Programming

    We propose a very simple preprocessing algorithm for semidefinite programming. Our algorithm inspects the constraints of the problem, deletes redundant rows and columns in the constraints, and reduces the size of the variable matrix. It often detects infeasibility. Our algorithm does not rely on any optimization solver: the only subroutine it needs is Cholesky factorization, … Read more

    Globally Optimized Finite Packings of Arbitrary Size Spheres in R^d

  • Ignacio Castillo
  • Frank J. Kampas
  • János Pintér
    • Categories Applications - Science and Engineering, Global Optimization Applications, Optimization Software Benchmark

    This work discusses the following general packing problem-class: given a finite collection of d-dimensional spheres with arbitrarily chosen radii, find the smallest sphere in R^d that contains the entire collection of these spheres in a non-overlapping arrangement. Generally speaking, analytical solution approaches cannot be expected to apply to this general problem-type, except for very small … Read more