Bound-constrained Optimization

On the application of the spectral projected gradient method in image segmentation

  • Laura Antonelli
  • Valentina De Simone
  • Daniela di Serafino
    • Categories Applications - Science and Engineering, Bound-constrained Optimization Tags , ,

    We investigate the application of the nonmonotone spectral projected gradient (SPG) method to a region-based variational model for image segmentation. We consider a “discretize-then-optimize” approach and solve the resulting nonlinear optimization problem by an alternating minimization procedure that exploits the SPG2 algorithm by Birgin, Martì­nez and Raydan (SIAM J. Optim., 10(4), 2000). We provide a … Read more

    Object-Parallel Infrastructure for Implementing First-Order Methods, with an Example Application to LASSO

  • Jonathan Eckstein
  • Gyorgy Matyasfalvi
    • Categories Bound-constrained Optimization, Parallel Algorithms, Unconstrained Optimization Tags , ,

    We describe the design of a C++ vector-manipulation substrate that allows first-order optimization algorithms to be expressed in a concise and readable manner, yet still achieve high performance in parallel computing environments. We use standard object-oriented techniques of encapsulation and operator overloading, combined with a novel “symbolic temporaries” delayed-evaluation system that greatly reduces the overhead … Read more

    A trust-region method for box-constrained nonlinear semidefinite programs

  • Akihiko Komatsu
  • Makoto Yamashita
    • Categories Bound-constrained Optimization, Semi-definite Programming Tags ,

    We propose a trust-region method for nonlinear semidefinite programs with box-constraints. The penalty barrier method can handle this problem, but the size of variable matrices available in practical time is restricted to be less than 500. We develop a trust-region method based on the approach of Coleman and Li (1996) that utilizes the distance to … Read more

    RBFOpt: an open-source library for black-box optimization with costly function evaluations

  • Alberto Costa
  • Giacomo Nannicini
    • Categories Bound-constrained Optimization, Global Optimization, Optimization Software and Modeling Systems

    We consider the problem of optimizing an unknown function given as an oracle over a mixed-integer box-constrained set. We assume that the oracle is expensive to evaluate, so that estimating partial derivatives by finite differences is impractical. In the literature, this is typically called a black-box optimization problem with costly evaluation. This paper describes the … Read more

    Monomial-wise Optimal Separable Underestimators for Mixed-Integer Polynomial Optimization

  • Christoph Buchheim
  • Claudia D'Ambrosio
    • Categories (Mixed) Integer Nonlinear Programming, Bound-constrained Optimization, Global Optimization

    In this paper we introduce a new method for solving box-constrained mixed-integer polynomial problems to global optimality. The approach, a specialized branch-and-bound algorithm, is based on the computation of lower bounds provided by the minimization of separable underestimators of the polynomial objective function. The underestimators are the novelty of the approach because the standard approaches … Read more

    On the Incomplete Oblique Projections Method for Solving Box Constrained Least Squares Problems

  • N. Echebest
  • MT Guardarucci
  • HD Scolnik
    • Categories Bound-constrained Optimization, Nonlinear Systems and Least-Squares Tags , ,

    The aim of this paper is to extend the applicability of the incomplete oblique projections method (IOP) previously introduced by the authors for solving inconsistent linear systems to the box constrained case. The new algorithm employs incomplete projections onto the set of solutions of the augmented system Ax-r= b, together with the box constraints, based … Read more

    A New Framework for Combining Global and Local Methods in Black Box Optimization

  • Yibo Ji
  • Sujin Kim
  • Wendy Lu Xu
    • Categories Applications - OR and Management Sciences, Bound-constrained Optimization, Global Optimization

    We propose a new framework for the optimization of computationally expensive black box problems, where neither closed-form expressions nor derivatives of the objective functions are available. The proposed framework consists of two procedures. The first constructs a global metamodel to approximate the underlying black box function and explores an unvisited area to search for a … Read more

    A matrix-free approach to build band preconditioners for large-scale bound-constrained optimization

  • Valentina De Simone
  • Daniela di Serafino
    • Categories Bound-constrained Optimization, Nonlinear Optimization

    We propose a procedure for building symmetric positive definite band preconditioners for large-scale symmetric, possibly indefinite, linear systems, when the coefficient matrix is not explicitly available, but matrix-vector products involving it can be computed. We focus on linear systems arising in Newton-type iterations within matrix-free versions of projected methods for bound-constrained nonlinear optimization. In this … Read more

    On the evaluation complexity of constrained nonlinear least-squares and general constrained nonlinear optimization using second-order methods

  • Coralia Cartis
  • Nicholas I. M. Gould
  • Philippe L. Toint
    • Categories Bound-constrained Optimization, Constrained Nonlinear Optimization, Nonlinear Systems and Least-Squares Tags , ,

    When solving the general smooth nonlinear optimization problem involving equality and/or inequality constraints, an approximate first-order critical point of accuracy $\epsilon$ can be obtained by a second-order method using cubic regularization in at most $O(\epsilon^{-3/2})$ problem-functions evaluations, the same order bound as in the unconstrained case. This result is obtained by first showing that the … Read more

    Subspace accelerated matrix splitting algorithms for bound-constrained quadratic programming and linear complementarity problems

  • Liming Feng
  • Jorge Nocedal
  • Daniel P. Robinson
  • Jong-Shi Pang
    • Categories Bound-constrained Optimization, Finance and Economics Tags , , , , , , ,

    This paper studies the solution of two problems—bound-constrained quadratic programs and linear complementarity problems—by two-phase methods that consist of an active set prediction phase and a subspace phase. The algorithms enjoy favorable convergence properties under weaker assumptions than those assumed for other methods in the literature. The active set prediction phase employs matrix splitting iterations … Read more