Nonlinear Optimization

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

    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

    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

    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

    Lagrange Multipliers with Optimal Sensitivity Properties

  • Dimitri Bertsekas
    • Categories Constrained Nonlinear Optimization Tags ,

    We consider optimization problems with inequality and abstract set constraints, and we derive sensitivity properties of Lagrange multipliers under very weak conditions. In particular, we do not assume uniqueness of a Lagrange multiplier or continuity of the perturbation function. We show that the Lagrange multiplier of minimum norm defines the optimal rate of improvement of … Read more

    The Design and Implementation of a Generic Sparse Bundle Adjustment Software Package Based on the Levenberg-Marquardt Algorithm

  • Antonis Argyros
  • Manolis Lourakis
    • Categories Basic Sciences Applications, Nonlinear Systems and Least-Squares, Optimization Software and Modeling Systems Tags , , , , ,

    Bundle adjustment using the Levenberg-Marquardt minimization algorithm is almost invariably used as the last step of every feature-based structure and motion estimation computer vision algorithm to obtain optimal 3D structure and viewing parameter estimates. However, due to the large number of unknowns contributing to the minimized reprojection error, a general purpose implementation of the Levenberg-Marquardt … Read more

    Sums of Squares and Semidefinite Programming Relaxations for Polynomial Optimization Problems with Structured Sparsity

  • Sunyoung Kim
  • Masakazu Kojima
  • Masakazu Muramatsu
  • Hayato Waki
    • Categories Constrained Nonlinear Optimization, Global Optimization, Linear, Cone and Semidefinite Programming Tags , , , , , ,

    Unconstrained and inequality constrained sparse polynomial optimization problems (POPs) are considered. A correlative sparsity pattern graph is defined to find a certain sparse structure in the objective and constraint polynomials of a POP. Based on this graph, sets of supports for sums of squares (SOS) polynomials that lead to efficient SOS and semidefinite programming (SDP) … Read more

    Best approximation to common fixed points of a semigroup of nonexpansive operators

  • Arkady Aleyner
  • Yair Censor
    • Categories Constrained Nonlinear Optimization, Convex and Nonsmooth Optimization Tags , , , ,

    We study a sequential algorithm for finding the projection of a given point onto the common fixed points set of a semigroup of nonexpansive operators in Hilbert space. The convergence of such an algorithm was previously established only for finitely many nonexpansive operators. Algorithms of this kind have been applied to the best approximation and … Read more