Optimization Software and Modeling Systems

Minimal Residual Methods for Complex Symmetric, Skew Symmetric, and Skew Hermitian Systems

  • Sou-Cheng Choi
    • Categories Convex Optimization, Optimization Software and Modeling Systems, Robust Optimization Tags , , , , , , , , , , , ,

    While there is no lack of efficient Krylov subspace solvers for Hermitian systems, there are few for complex symmetric, skew symmetric, or skew Hermitian systems, which are increasingly important in modern applications including quantum dynamics, electromagnetics, and power systems. For a large consistent complex symmetric system, one may apply a non-Hermitian Krylov subspace method disregarding … Read more

    CUTEst: a Constrained and Unconstrained Testing Environment with safe threads

  • Nicholas I. M. Gould
  • Dominique Orban
  • Philippe L. Toint
    • Categories Optimization Software and Modeling Systems Tags ,

    We describe the most recent evolution of our constrained and unconstrained testing environment and its accompanying SIF decoder. Code-named SIFDecode and CUTEst, these updated versions feature dynamic memory allocation, a modern thread-safe Fortran modular design, a new Matlab interface and a revised installation procedure integrated with GALAHAD. Citation Technical Report Rutherford Appleton Laboratory Chilton, Oxfordshire, … Read more

    Trace-Penalty Minimization for Large-scale Eigenspace Computation

  • Xin Liu
  • Zaiwen Wen
  • Yin Zhang
  • Chao Yang
    • Categories Basic Sciences Applications, Constrained Nonlinear Optimization, Parallel Algorithms Tags , ,

    The Rayleigh-Ritz (RR) procedure, including orthogonalization, constitutes a major bottleneck in computing relatively high dimensional eigenspaces of large sparse matrices. Although operations involved in RR steps can be parallelized to a certain level, their parallel scalability, which is limited by some inherent sequential steps, is lower than dense matrix-matrix multiplications. The primary motivation of this … Read more

    Embedded Online Optimization for Model Predictive Control at Megahertz Rates

  • George A. Constantinides
  • Paul J. Goulart
  • Eric C. Kerrigan
  • Stefan Richter
  • Juan L. Jerez
  • Manfred Morari
    • Categories Parallel Algorithms, Quadratic Programming Tags , ,

    Faster, cheaper, and more power efficient optimization solvers than those currently offered by general-purpose solutions are required for extending the use of model predictive control (MPC) to resource-constrained embedded platforms. We propose several custom computational architectures for different first-order optimization methods that can handle linear-quadratic MPC problems with input, input-rate, and soft state constraints. We … Read more

    A framework for automated PDE-constrained optimisation

  • P. E. Farrell
  • S. W. Funke
    • Categories Problem Solving Environments Tags , , , , ,

    A generic framework for the solution of PDE-constrained optimisation problems based on the FEniCS system is presented. Its main features are an intuitive mathematical interface, a high degree of automation, and an efficient implementation of the generated adjoint model. The framework is based upon the extension of a domain-specific language for variational problems to cleanly … Read more

    Computational aspects of simplex and MBU-simplex algorithms using different anti-cycling pivot rules

  • Nagy Adrienn
  • Tibor Illés
    • Categories Linear Programming, Optimization Software Benchmark Tags , , ,

    Several variations of index selection rules for simplex type algorithms for linear programming, like the Last-In-First-Out or the Most-Often-Selected-Variable are rules not only theoretically finite, but also provide significant flexibility in choosing a pivot element. Based on an implementation of the primal simplex and the monotonic build-up (MBU) simplex method, the practical benefit of the … Read more

    Biased and unbiased random-key genetic algorithms: An experimental analysis

  • José Fernando Gonçalves
  • Mauricio G.C. Resende
  • Rodrigo F. Toso
    • Categories Meta Heuristics, Optimization Software Benchmark, Stochastic Approaches Tags , , , , , ,

    We study the runtime performance of three types of random-key genetic algorithms: the unbiased algorithm of Bean (1994); the biased algorithm of Gonçalves and Resende (2011); and a greedy version of Bean’s algorithm on 12 instances from four types of covering problems: general-cost set covering, Steiner triple covering, general-cost set K-covering, and unit-cost covering by … Read more

    ALGORITHM & DOCUMENTATION: MINRES-QLP for Singular Symmetric and Hermitian Linear Equations and Least-Squares Problems

  • Sou-Cheng Choi
    • Categories Applications - OR and Management Sciences, Applications - Science and Engineering, Optimization Software and Modeling Systems Tags , , , , , , , , ,

    We describe algorithm MINRES-QLP and its FORTRAN 90 implementation for solving symmetric or Hermitian linear systems or least-squares problems. If the system is singular, MINRES-QLP computes the unique minimum-length solution (also known as the pseudoinverse solution), which generally eludes MINRES. In all cases, it overcomes a potential instability in the original MINRES algorithm. A positive-definite … Read more

    VSDP: A Matlab toolbox for verified semidefinite-quadratic-linear programming

  • Viktor Härter
  • Christian Jansson
  • Marko Lange
    • Categories Linear, Cone and Semidefinite Programming, Optimization Software and Modeling Systems Tags , , , ,

    VSDP is a software package that is designed for the computation of verified results in conic programming. The current version of VSDP supports the constraint cone consisting of the product of semidefinite cones, second-order cones and the nonnegative orthant. It provides functions for computing rigorous error bounds of the true optimal value, verified enclosures of … Read more

    Parallel Coordinate Descent Methods for Big Data Optimization

  • Peter Richtarik
  • Martin Takac
    • Categories Convex Optimization, Parallel Algorithms Tags , , , , , , , ,

    In this work we show that randomized (block) coordinate descent methods can be accelerated by parallelization when applied to the problem of minimizing the sum of a partially separable smooth convex function and a simple separable convex function. The theoretical speedup, as compared to the serial method, and referring to the number of iterations needed … Read more