Nonlinear Optimization

On the Global Convergence of a Trust Region Method for Solving Nonlinear Constraints Infeasibility Problem

  • Choong Ming Chin
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization, Nonlinear Systems and Least-Squares Tags , , , ,

    A framework for proving global convergence for a class of nonlinear constraints infeasibility problem is presented without assuming that the Jacobian has full rank everywhere. The underlying method is based on the simple sufficient reduction criteria where trial points are accepted provided there is a sufficient decrease in the constraints violation function. The proposed methods … Read more

    Set Intersection Theorems and Existence of Optimal Solutions

  • Dimitri Bertsekas
  • Paul Tseng
    • Categories Constrained Nonlinear Optimization, Convex Optimization Tags , , ,

    The question of nonemptiness of the intersection of a nested sequence of closed sets is fundamental in a number of important optimization topics, including the existence of optimal solutions, the validity of the minimax inequality in zero sum games, and the absence of a duality gap in constrained optimization. We introduce the new notion of … Read more

    Interior Methods for Mathematical Programs with Complementarity Constraints

  • Sven Leyffer
  • Gabriel Lopez-Calva
  • Jorge Nocedal
    • Categories Complementarity and Variational Inequalities, Constrained Nonlinear Optimization Tags , , , , , ,

    This paper studies theoretical and practical properties of interior-penalty methods for mathematical programs with complementarity constraints. A framework for implementing these methods is presented, and the need for adaptive penalty update strategies is motivated with examples. The algorithm is shown to be globally convergent to strongly stationary points, under standard assumptions. These results are then … Read more

    Steering Exact Penalty Methods for Optimization

  • Richard H. Byrd
  • Jorge Nocedal
  • Richard A. Waltz
    • Categories Nonlinear Optimization Tags ,

    This paper reviews, extends and analyzes a new class of penalty methods for nonlinear optimization. These methods adjust the penalty parameter dynamically; by controlling the degree of linear feasibility achieved at every iteration, they promote balanced progress toward optimality and feasibility. In contrast with classical approaches, the choice of the penalty parameter ceases to be … Read more

    Convergence Analysis of an Interior-Point Method for Mathematical Programs with Equilibrium Constraints

  • Arun Sen
  • David F. Shanno
    • Categories Complementarity and Variational Inequalities, Constrained Nonlinear Optimization Tags , , ,

    We prove local and global convergence results for an interior-point method applied to mathematical programs with equilibrium constraints. The global result shows the algorithm minimizes infeasibility regardless of starting point, while one result proves local convergence when penalty functions are exact; another local result proves convergence when the solution is not even a KKT point. … Read more

    Algorithm xxx: APPSPACK 4.0: Asynchronous Parallel Pattern Search for Derivative-Free Optimization

  • Genetha Gray
  • Tamara Kolda
    • Categories Bound-constrained Optimization, Optimization Software and Modeling Systems, Parallel Algorithms Tags , , ,

    APPSPACK is software for solving unconstrained and bound constrained optimization problems. It implements an asynchronous parallel pattern search method that has been specifically designed for problems characterized by expensive function evaluations. Using APPSPACK to solve optimization problems has several advantages: No derivative information is needed; the procedure for evaluating the objective function can be executed … Read more

    Computational experience with an interior point algorithm for large scale contact problems

  • Dominikus Noll
  • Y. Renard
  • G. Tanoh
    • Categories Constrained Nonlinear Optimization, Mechanical Engineering, Quadratic Programming Tags , , ,

    In this paper we present an interior point method for large scale Signorini elastic contact problems. We study the case of an elastic body in frictionless contact with a rigid foundation. Primal and primal-dual algorithms are developed to solve the quadratic optimization problem arising in the variational formulation. Our computational study confirms the efficiency of … Read more

    Using Sampling and Simplex Derivatives in Pattern Search Methods

  • Ana Luisa Custódio
  • Luis Nunes Vicente
    • Categories Nonlinear Optimization Tags , , , , ,

    Pattern search methods can be made more efficient if past function evaluations are appropriately reused. In this paper we will introduce a number of ways of reusing previous evaluations of the objective function based on the computation of simplex derivatives (e.g., simplex gradients) to improve the efficiency of a pattern search iteration. At each iteration … Read more

    Magnetic Resonance Tissue Density Estimation using Optimal SSFP Pulse-Sequence Design

  • Christopher Anand
  • Renata Sotirov
  • Tamás Terlaky
  • Zhuo Zheng
    • Categories Linear, Cone and Semidefinite Programming, Nonlinear Optimization Tags , , , ,

    In this paper, we formulate a nonlinear, nonconvex semidefinite optimization problem to select the steady-state free precession (SSFP) pulse-sequence design variables which maximize the contrast to noise ratio in tissue segmentation. The method could be applied to other pulse sequence types, arbitrary numbers of tissues, and numbers of images. To solve the problem we use … Read more

    Finding optimal algorithmic parameters using a mesh adaptive direct search

  • Charles Audet
  • Dominique Orban
    • Categories Nonlinear Optimization, Nonsmooth Optimization, Unconstrained Optimization Tags , , , , ,

    The objectives of this paper are twofold; we first demonstrate the flexibility of the mesh adaptive direct search (MADS) in identifying locally optimal algorithmic parameters. This is done by devising a general framework for parameter tuning. The framework makes provision for surrogate objectives. Parameters are sought so as to minimize some measure of performance of … Read more