Constrained Nonlinear Optimization

A globally convergent trust-region SQP method without a penalty function for nonlinearly constrained optimization

  • Hiroshi Yabe
  • Hiroshi Yamashita
    • Categories Constrained Nonlinear Optimization Tags , ,

    In this paper, we propose a new trust-region SQP method, which uses no penalty function, for solving nonlinearly constrained optimization problem. Our method consists of alternate two phases. Specifically, we alternately proceed the feasibility restoration phase and the objective function minimization phase. The global convergence property of the proposed method is shown. Citation Cooperative Research … Read more

    A primal-dual interior point method for nonlinear semidefinite programming

  • Kouhei Harada
  • Hiroshi Yabe
  • Hiroshi Yamashita
    • Categories Constrained Nonlinear Optimization Tags , , , ,

    In this paper, we consider a primal-dual interior point method for solving nonlinear semidefinite programming problems. By combining the primal barrier penalty function and the primal-dual barrier function, a new primal-dual merit function is proposed within the framework of the line search strategy. We show the global convergence property of our method. Finally some numerical … Read more

    Convergence Analysis of an Interior-Point Method for Nonconvex Nonlinear Programming

  • Hande Benson
  • Arun Sen
  • David F. Shanno
    • Categories Constrained Nonlinear Optimization Tags , ,

    In this paper, we present global and local convergence results for an interior-point method for nonlinear programming. The algorithm uses an $\ell_1$ penalty approach to relax all constraints, to provide regularization, and to bound the Lagrange multipliers. The penalty problems are solved using a simplified version of Chen and Goldfarb’s strictly feasible interior-point method [6]. … Read more

    An implicit trust-region method on Riemannian manifolds

  • Pierre-Antoine Absil
  • Kyle A. Gallivan
  • C. G. Baker
    • Categories Constrained Nonlinear Optimization Tags , ,

    We propose and analyze an “implicit” trust-region method in the general setting of Riemannian manifolds. The method is implicit in that the trust-region is defined as a superlevel set of the ratio of the actual over predicted decrease in the objective function. Since this method potentially requires the evaluation of the objective function at each … Read more

    Self-concordant Tree and Decomposition Based Interior Point Methods for Stochastic Convex Optimization Problem

  • Michael Chen
  • Sanjay Mehrotra
    • Categories Constrained Nonlinear Optimization, Stochastic Programming

    We consider barrier problems associated with two and multistage stochastic convex optimization problems. We show that the barrier recourse functions at any stage form a self-concordant family with respect to the barrier parameter. We also show that the complexity value of the first stage problem increases additively with the number of stages and scenarios. We … Read more

    A Coordinate Gradient Descent Method for Linearly Constrained Smooth Optimization and Support Vector Machines Training

  • Paul Tseng
  • Sangwoon Yun
    • Categories Constrained Nonlinear Optimization, Data-Mining Tags , , , , , , , ,

    Support vector machines (SVMs) training may be posed as a large quadratic program (QP) with bound constraints and a single linear equality constraint. We propose a (block) coordinate gradient descent method for solving this problem and, more generally, linearly constrained smooth optimization. Our method is closely related to decomposition methods currently popular for SVM training. … Read more

    Nonlinear programming without a penalty function or a filter

  • Nicholas I. M. Gould
  • Philippe L. Toint
    • Categories Constrained Nonlinear Optimization, Nonlinear Systems and Least-Squares, Systems governed by Differential Equations Optimization Tags , , ,

    A new method is introduced for solving equality constrained nonlinear optimization problems. This method does not use a penalty function, nor a barrier or a filter, and yet can be proved to be globally convergent to first-order stationary points. It uses different trust-regions to cope with the nonlinearities of the objective function and the constraints, … Read more

    A null-space primal-dual interior-point algorithm for nonlinear optimization with nice convergence properties

  • Xin-Wei Liu
  • Ya-xiang Yuan
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags , , ,

    We present a null-space primal-dual interior-point algorithm for solving nonlinear optimization problems with general inequality and equality constraints. The algorithm approximately solves a sequence of equality constrained barrier subproblems by computing a predictor step and a null space step in every iteration. The $\ell_2$ penalty function is taken as the merit function. Under very mild … Read more

    Approximate Primal Solutions and Rate Analysis in Dual Subgradient Methods

  • Angelia Nedich
  • Asuman Ozdaglar
    • Categories Constrained Nonlinear Optimization, Convex Optimization, Nonsmooth Optimization Tags , , , ,

    We study primal solutions obtained as a by-product of subgradient methods when solving the Lagrangian dual of a primal convex constrained optimization problem (possibly nonsmooth). The existing literature on the use of subgradient methods for generating primal optimal solutions is limited to the methods producing such solutions only asymptotically (i.e., in the limit as the … Read more

    Finding a point in the relative interior of a polyhedron

  • Coralia Cartis
  • Nicholas I. M. Gould
    • Categories Constrained Nonlinear Optimization, Linear Programming Tags ,

    A new initialization or `Phase I’ strategy for feasible interior point methods for linear programming is proposed that computes a point on the primal-dual central path associated with the linear program. Provided there exist primal-dual strictly feasible points — an all-pervasive assumption in interior point method theory that implies the existence of the central path … Read more