Optimization Software and Modeling Systems

Data Fitting and Experimental Design in Dynamical Systems with EASY-FIT ModelDesign

  • Klaus Schittkowski
    • Categories Nonlinear Systems and Least-Squares, Problem Solving Environments, Systems governed by Differential Equations Optimization

    EASY-FIT is an interactive software system to identify parameters and compute optimal designs in explicit model functions, steady-state systems, 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. Proceeding from given experimental data, i.e. observation times and measurements, the minimum … Read more

    An Updated Set of 306 Test Problems for Nonlinear Programming with Validated Optimal Solutions

  • Klaus Schittkowski
    • Categories Constrained Nonlinear Optimization, Optimization Software Benchmark

    The availability of nonlinear programming test problems is extremely important to test optimization codes or to develop new algorithms. We describe the usage of the Fortran subroutines for all 306 test problems of two previous collections of the author, see Hock and Schittkowski (1981) and Schittkowski (1987). For each test example, we provide an optimal … Read more

    PARNES: A rapidly convergent algorithm for accurate recovery of sparse and approximately sparse signals

  • Ming Gu
  • Lek-Heng Lim
  • Cinna Julie Wu
    • Categories Constrained Nonlinear Optimization, Convex Optimization, Optimization Software Benchmark Tags , , , , , , ,

    In this article we propose an algorithm, NESTA-LASSO, for the LASSO problem (i.e., an underdetermined linear least-squares problem with a one-norm constraint on the solution) that exhibits linear convergence under the restricted isometry property (RIP) and some other reasonable assumptions. Inspired by the state-of-the-art sparse recovery method, NESTA, we rely on an accelerated proximal gradient … Read more

    Stopping rules and backward error analysis for bound-constrained optimization

  • Serge Gratton
  • Philippe L. Toint
  • Mélodie Mouffe
    • Categories Bound-constrained Optimization, Optimization Software Design Principles Tags , , , ,

    Termination criteria for the iterative solution of bound-constrained optimization problems are examined in the light of backward error analysis. It is shown that the problem of determining a suitable perturbation on the problem’s data corresponding to the definition of the backward error is analytically solvable under mild assumptions. Moreover, a link between existing termination criteria … Read more

    Code verification by static analysis: a mathematical programming approach

  • Stephane Le Roux
  • Leo Liberti
  • Fabrizio Marinelli
  • Jeremy Leconte
    • Categories (Mixed) Integer Nonlinear Programming, Applications - Science and Engineering, Modeling Languages and Systems Tags , , , , ,

    Automatic verification of computer code is of paramount importance in embedded systems supplying essential services. One of the most important verification techniques is static code analysis by abstract interpretation: the concrete semantics of a programming language (i.e.the values $\chi$ that variable symbols {\tt x} appearing in a program can take during its execution) are replaced … Read more

    Robust Optimization Made Easy with ROME

  • Joel Goh
  • Melvyn Sim
    • Categories Modeling Languages and Systems, Robust Optimization Tags ,

    We introduce an algebraic modeling language, named ROME, for a class of robust optimization problems. ROME serves as an intermediate layer between the modeler and optimization solver engines, allowing modelers to express robust optimization problems in a mathematically meaningful way. In this paper, we highlight key features of ROME which expediates the modeling and subsequent … Read more

    Algorithm 909: NOMAD: Nonlinear Optimization with the MADS algorithm

  • Sébastien Le Digabel
    • Categories Applications - OR and Management Sciences, Optimization Software and Modeling Systems Tags , , , ,

    NOMAD is software that implements the MADS algorithm (Mesh Adaptive Direct Search) for black-box optimization under general nonlinear constraints. Blackbox optimization is about optimizing functions that are usually given as costly programs with no derivative information and no function values returned for a significant number of calls attempted. NOMAD is designed for such problems and … Read more

    On String-Averaging for Sparse Problems and On the Split Common Fixed Point Problem

  • Yair Censor
  • Alexander Segal
    • Categories Nonlinear Optimization, Parallel Algorithms Tags , ,

    We review the common fixed point problem for the class of directed operators. This class is important because many commonly used nonlinear operators in convex optimization belong to it. We present our recent definition of sparseness of a family of operators and discuss a string-averaging algorithmic scheme that favorably handles the common fixed points problem … Read more

    Semidefinite programming and sums of hermitian squares of noncommutative polynomials

  • Igor Klep
  • Janez Povh
    • Categories Optimization Software Design Principles, Semi-definite Programming Tags , , ,

    An algorithm for finding sums of hermitian squares decompositions for polynomials in noncommuting variables is presented. The algorithm is based on the “Newton chip method”, a noncommutative analog of the classical Newton polytope method, and semide finite programming. Citation I. Klep and J. Povh. Semide nite programming and sums of hermitian squares of noncommutative polynomials. J. Pure … Read more

    A Structure-Conveying Modelling Language for Mathematical and Stochastic Programming

  • Marco Colombo
  • Jacek Gondzio
  • Andreas Grothey
  • Jonathan Hogg
  • Kristian Woodsend
    • Categories Modeling Languages and Systems Tags , , ,

    We present a structure-conveying algebraic modelling language for mathematical programming. The proposed language extends AMPL with object-oriented features that allows the user to onstruct models from sub-models, and is implemented as a combination of pre- and post-processing phases for AMPL. Unlike traditional modelling languages, the new approach does not scramble the block structure of the … Read more