global convergence

A second-order optimality condition with first- and second-order complementarity associated with global convergence of algorithms

  • Gabriel Haeser
    • Categories Constrained Nonlinear Optimization Tags , , ,

    We develop a new notion of second-order complementarity with respect to the tangent subspace related to second-order necessary optimality conditions by the introduction of so-called tangent multipliers. We prove that around a local minimizer, a second-order stationarity residual can be driven to zero while controlling the growth of Lagrange multipliers and tangent multipliers, which gives … Read more

    A recursive semi-smooth Newton method for linear complementarity problems

  • Philipp Hungerländer
  • Joaquim J. Júdice
  • Franz Rendl
    • Categories Bound-constrained Optimization, Convex Optimization, Quadratic Programming Tags , , , ,

    A primal feasible active set method is presented for finding the unique solution of a Linear Complementarity Problem (LCP) with a P-matrix, which extends the globally convergent active set method for strictly convex quadratic problems with simple bounds proposed by [P. Hungerlaender and F. Rendl. A feasible active set method for strictly convex problems with … Read more

    A New Trust Region Method with Simple Model for Large-Scale Optimization

  • Wenyu Sun
  • Hongchao Zhang
  • Qunyan Zhou
    • Categories Unconstrained Optimization Tags , , , ,

    In this paper a new trust region method with simple model for solving large-scale unconstrained nonlinear optimization problems is proposed. By using the generalized weak quasi-Newton equations, we derive several schemes to determine the appropriate scalar matrix as the Hessian approximation. Under some reasonable conditions and the framework of the trust-region method, the global convergence … Read more

    Global convergence of a derivative-free inexact restoration filter algorithm for nonlinear programming

  • Priscila Savulski Ferreira
  • Elizabeth Wegner Karas
  • Mael Sachine
  • Francisco N. C. Sobral
    • Categories Constrained Nonlinear Optimization Tags , , , , ,

    In this work we present an algorithm for solving constrained optimization problems that does not make explicit use of the objective function derivatives. The algorithm mixes an inexact restoration framework with filter techniques, where the forbidden regions can be given by the flat or slanting filter rule. Each iteration is decomposed in two independent phases: … Read more

    Global Convergence of Unmodified 3-Block ADMM for a Class of Convex Minimization Problems

  • Tianyi Lin
  • Shiqian Ma
  • Shuzhong Zhang
    • Categories Convex and Nonsmooth Optimization Tags , , ,

    The alternating direction method of multipliers (ADMM) has been successfully applied to solve structured convex optimization problems due to its superior practical performance. The convergence properties of the 2-block ADMM have been studied extensively in the literature. Specifically, it has been proven that the 2-block ADMM globally converges for any penalty parameter $\gamma>0$. In this … Read more

    A corrected semi-proximal ADMM for multi-block convex optimization and its application to DNN-SDPs

  • Shaohua Pan
  • Li Shen
    • Categories Convex Optimization, Linear, Cone and Semidefinite Programming Tags , , ,

    In this paper we propose a corrected semi-proximal ADMM (alternating direction method of multipliers) for the general $p$-block $(p\!\ge 3)$ convex optimization problems with linear constraints, aiming to resolve the dilemma that almost all the existing modified versions of the directly extended ADMM, although with convergent guarantee, often perform substantially worse than the directly extended … Read more

    A Parallel Evolution Strategy for an Earth Imaging Problem in Geophysics

  • H. Calandra
  • Serge Gratton
  • Luis Nunes Vicente
  • Y. Diouane
  • X. Vasseur
    • Categories Basic Sciences Applications, Global Optimization Applications, Optimization of Simulated Systems Tags , , , , , ,

    In this paper we propose a new way to compute a warm starting point for a challenging global optimization problem related to Earth imaging in geophysics. The warm start consists of a velocity model that approximately solves a full-waveform inverse problem at low frequency. Our motivation arises from the availability of massively parallel computing platforms … Read more

    A Trust Region Algorithm with a Worst-Case Iteration Complexity of ${\cal O}(\epsilon^{-3/2})$ for Nonconvex Optimization

  • Frank E. Curtis
  • Daniel P. Robinson
  • Mohammadreza Samadi
    • Categories Nonlinear Optimization, Unconstrained Optimization Tags , , , , , , ,

    We propose a trust region algorithm for solving nonconvex smooth optimization problems. For any $\bar\epsilon \in (0,\infty)$, the algorithm requires at most $\mathcal{O}(\epsilon^{-3/2})$ iterations, function evaluations, and derivative evaluations to drive the norm of the gradient of the objective function below any $\epsilon \in (0,\bar\epsilon]$. This improves upon the $\mathcal{O}(\epsilon^{-2})$ bound known to hold for … Read more

    On efficiency of nonmonotone Armijo-type line searches

  • Masoud Ahookhosh
  • Susan Ghaderi
    • Categories Nonlinear Optimization, Unconstrained Optimization Tags , , , , ,

    Monotonicity and nonmonotonicity play a key role in studying the global convergence and the efficiency of iterative schemes employed in the field of nonlinear optimization, where globally convergent and computationally efficient schemes are explored. This paper addresses some features of descent schemes and the motivation behind nonmonotone strategies and investigates the efficiency of an Armijo-type … Read more

    Globally Convergent Evolution Strategies for Constrained Optimization.

  • Youssef Diouane
  • Serge Gratton
  • Luis Nunes Vicente
    • Categories Constrained Nonlinear Optimization Tags , , , , , , ,

    In this work we propose, analyze, and test algorithms for linearly constrained optimization when no use of derivatives of the objective function is made. The proposed methodology is built upon the globally convergent evolution strategies previously introduced by the authors for unconstrained optimization. Two approaches are encompassed to handle the constraints. In a first approach, … Read more