Optimization Software and Modeling Systems

On the implementation and usage of SDPT3 — a Matlab software package for semidefinite-quadratic-linear programming, version 4.0

  • Michael J. Todd
  • Kim-Chuan Toh
  • Reha H. Tütüncü
    • Categories Linear, Cone and Semidefinite Programming, Optimization Software and Modeling Systems

    This software is designed to solve primal and dual semidefinite-quadratic-linear conic programming problems (known as SQLP problems) whose constraint cone is a product of semidefinite cones, second-order cones, nonnegative orthants and Euclidean spaces, and whose objective function is the sum of linear functions and log-barrier terms associated with the constraint cones. This includes the special … Read more

    NCSOSTOOLS: A COMPUTER ALGEBRA SYSTEM FOR SYMBOLIC AND NUMERICAL COMPUTATION WITH NONCOMMUTATIVE POLYNOMIALS

  • Kristijan Cafuta
  • Igor Klep
  • Janez Povh
    • Categories Optimization Software and Modeling Systems, Semi-definite Programming Tags , , ,

    Abstract. NCSOStools is a Matlab toolbox for – symbolic computation with polynomials in noncommuting variables; – constructing and solving sum of hermitian squares (with commutators) programs for polynomials in noncommuting variables. It can be used in combination with semidefi nite programming software, such as SeDuMi, SDPA or SDPT3 to solve these constructed programs. This paper provides … Read more

    A preconditioning technique for Schur complement systems arising in stochastic optimization

  • Mihai Anitescu
  • Cosmin G. Petra
    • Categories Parallel Algorithms, Stochastic Programming

    Deterministic sample average approximations of stochastic programming problems with recourse are suitable for a scenario-based, treelike parallelization with interior-point methods and a Schur complement mechanism. However, the direct linear solves involving the Schur complement matrix are expensive, and adversely a ect the scalability of this approach. In this paper we propose a stochastic preconditioner to address … Read more

    The tracial moment problem and trace-optimization of polynomials

  • Sabine Burgdorf
  • Kristijan Cafuta
  • Igor Klep
  • Janez Povh
    • Categories Global Optimization, Optimization Software and Modeling Systems, Semi-definite Programming Tags , , , , , ,

    The main topic addressed in this paper is trace-optimization of polynomials in noncommuting (nc) variables: given an nc polynomial f, what is the smallest trace f(A) can attain for a tuple of matrices A? A relaxation using semidefinite programming (SDP) based on sums of hermitian squares and commutators is proposed. While this relaxation is not … Read more

    MINRES-QLP: a Krylov subspace method for indefinite or singular symmetric systems

  • Sou-Cheng Choi
  • Christopher Paige
  • Michael A. Saunders
    • Categories Convex Optimization, Optimization Software and Modeling Systems, Statistics Tags , , , , , , ,

    CG, SYMMLQ, and MINRES are Krylov subspace methods for solving symmetric systems of linear equations. When these methods are applied to an incompatible system (that is, a singular symmetric least-squares problem), CG could break down and SYMMLQ’s solution could explode, while MINRES would give a least-squares solution but not necessarily the minimum-length (pseudoinverse) solution. This … Read more

    Exploiting run time distributions to compare sequential and parallel stochastic local search algorithms

  • Celso C. Ribeiro
  • Isabel Rosseti
  • Reinaldo Vallejos
    • Categories Meta Heuristics, Parallel Algorithms, Stochastic Approaches

    Run time distributions or time-to-target plots are very useful tools to characterize the running times of stochastic algorithms for combinatorial optimization. We further explore run time distributions and describe a new tool to compare two algorithms based on stochastic local search. For the case where the running times of both algorithms fit exponential distributions, we … Read more

    Estimating Computational Noise

  • Jorge Moré
  • Stefan M. Wild
    • Categories Nonlinear Optimization, Optimization Software and Modeling Systems, Other Topics Tags , ,

    Computational noise in deterministic simulations is as ill-defined a concept as can be found in scientific computing. When coupled with adaptive strategies, the effects of finite precision destroy smoothness of the simulation output and complicate subsequent analysis. Following the work of Hamming on roundoff errors, we present a new algorithm, ECnoise, for quantifying the noise … Read more

    Python Optimization Modeling Objects (Pyomo)

  • William E. Hart
  • Jean-Paul Watson
  • David L. Woodruff
    • Categories (Mixed) Integer Linear Programming, Modeling Languages and Systems, Parallel Algorithms

    We describe Pyomo, an open source tool for modeling optimization applications in Python. Pyomo can be used to de fine symbolic problems, create concrete problem instances, and solve these instances with standard solvers. Pyomo provides a capability that is commonly associated with algebraic modeling languages such as AMPL, AIMMS, and GAMS, but Pyomo’s modeling objects are … Read more

    A Collection of 1,300 Dynamical Systems for Testing Data Fitting, Optimal Control, Experimental Design, Identification, Simulation or Similar Software – User’s Guide

  • Klaus Schittkowski
    • Categories Modeling Languages and Systems, Optimization Software Benchmark, Systems governed by Differential Equations Optimization

    We describe a collection of test problems which have been used to develop and test data fitting software for identifying parameters in explicit model functions, dynamical systems of equations, Laplace transformations, systems of ordinary differential equations, differential algebraic equations, or systems of one-dimensional time-dependent partial differential equations with or without algebraic equations. The test cases … Read more

    MathOptimizer: A nonlinear optimization package for Mathematica users

  • Frank J. Kampas
  • János Pintér
    • Categories Constrained Nonlinear Optimization, Global Optimization, Optimization Software and Modeling Systems

    Mathematica is an advanced software system that enables symbolic computing, numerics, program code development, model visualization and professional documentation in a unified framework. Our MathOptimizer software package serves to solve global and local optimization models developed using Mathematica. We introduce MathOptimizer’s key features and discuss its usage options that support a range of operational modes. … Read more