Constrained Nonlinear Optimization

Solution of monotone complementarity and general convex programming problems using modified potential reduction interior point method

  • Kuo-Ling Huang
  • Sanjay Mehrotra
    • Categories Constrained Nonlinear Optimization, Convex Optimization, Quadratic Programming Tags , , , ,

    We present a homogeneous algorithm equipped with a modified potential function for the monotone complementarity problem. We show that this potential function is reduced by at least a constant amount if a scaled Lipschitz condition is satis ed. A practical algorithm based on this potential function is implemented in a software package named iOptimize. The implementation … Read more

    Packing Ellipsoids with Overlap

  • Caroline Uhler
  • Stephen Wright
    • Categories Biomedical Applications, Constrained Nonlinear Optimization, Nonsmooth Optimization Tags , , ,

    The problem of packing ellipsoids of different sizes and shapes into an ellipsoidal container so as to minimize a measure of overlap between ellipsoids is considered. A bilevel optimization formulation is given, together with an algorithm for the general case and a simpler algorithm for the special case in which all ellipsoids are in fact … Read more

    On Differentiability Properties of Player Convex Generalized Nash Equilibrium Problems

  • Nadja Harms
  • Oliver Stein
  • Christian Kanzow
    • Categories Constrained Nonlinear Optimization, Game Theory, Nonsmooth Optimization Tags , , , , ,

    This article studies differentiability properties for a reformulation of a player convex generalized Nash equilibrium problem as a constrained and possibly nonsmooth minimization problem. By using several results from parametric optimization we show that, apart from exceptional cases, all locally minimal points of the reformulation are differentiability points of the objective function. This justifies a … Read more

    Limited Memory Block Krylov Subspace Optimization for Computing Dominant Singular Value Decompositions

  • Xin Liu
  • Zaiwen Wen
  • Yin Zhang
    • Categories Constrained Nonlinear Optimization, Data-Mining Tags , , ,

    In many data-intensive applications, the use of principal component analysis (PCA) and other related techniques is ubiquitous for dimension reduction, data mining or other transformational purposes. Such transformations often require efficiently, reliably and accurately computing dominant singular value decompositions (SVDs) of large unstructured matrices. In this paper, we propose and study a subspace optimization technique … Read more

    Stochastic Optimization Approach to Water Management in Cooling-Constrained Power Plants

  • Emil M. Constantinescu
  • Victor M. Zavala
  • Urmila Diwekar
  • Juan M. Salazar
    • Categories Applications - OR and Management Sciences, Constrained Nonlinear Optimization, Stochastic Programming

    We propose a stochastic optimization framework to perform water management in coolingconstrained power plants. The approach determines optimal set-points to maximize power output in the presence of uncertain weather conditions and water intake constraints. Weather uncertainty is quantified in the form of ensembles using the state-of-the-art numerical weather prediction model WRF. The framework enables us … Read more

    On optimizing the sum of the Rayleigh quotient and the generalized Rayleigh quotient on the unit sphere

  • Zhang Lei-Hong
    • Categories Applications - Science and Engineering, Constrained Nonlinear Optimization, Global Optimization Tags , , , ,

    Given symmetric matrices $B,D\in R^{n\times n}$ and a symmetric positive definite matrix $W\in R^{n\times n},$ maximizing the sum of the Rayleigh quotient $x^T Dx$ and the generalized Rayleigh quotient $x^T Bx/x^TWx$ on the unit sphere not only is of mathematical interest in its own right, but also finds applications in practice. In this paper, we … Read more

    On Relaxing the Mangasarian-Fromovitz Constraint Qualification

  • Alexander Y. Kruger
  • Jiri V. Outrata
  • Leonid Minchenko
    • Categories Constrained Nonlinear Optimization

    For the classical nonlinear program two new relaxations of the Mangasarian-Fromovitz constraint qualification are discussed and their relationship with some standard constraint qualifications is examined. In particular, we establish the equivalence of one of these constraint qualifications with the recently suggested by Andreani et al. Constant rank of the subspace component constraint qualification. As an … Read more

    Interior-Point Methods for Nonconvex Nonlinear Programming: Cubic Regularization

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

    In this paper, we present a barrier method for solving nonlinear programming problems. It employs a Levenberg-Marquardt perturbation to the Karush-Kuhn-Tucker (KKT) matrix to handle indefinite Hessians and a line search to obtain sufficient descent at each iteration. We show that the Levenberg-Marquardt perturbation is equivalent to replacing the Newton step by a cubic regularization … Read more

    NUMERICAL OPTIMIZATION METHODS FOR BLIND DECONVOLUTION

  • Anastasia Cornelio
  • Elena Loli Piccolomini
  • James G. Nagy
    • Categories Constrained Nonlinear Optimization, Nonlinear Systems and Least-Squares Tags , , , ,

    This paper describes a nonlinear least squares framework to solve a separable nonlinear ill-posed inverse problems that arises in blind deconvolution. It is shown that with proper constraints and well chosen regularization parameters, it is possible to obtain an objective function that is fairly well behaved and the nonlinear minimization problem can be effectively solved … Read more

    Interior Point Methods for Optimal Experimental Designs

  • Zhaosong Lu
  • Ting Kei Pong
    • Categories Constrained Nonlinear Optimization, Semi-definite Programming, Statistics Tags , , , , ,

    In this paper, we propose a primal IP method for solving the optimal experimental design problem with a large class of smooth convex optimality criteria, including A-, D- and p th mean criterion, and establish its global convergence. We also show that the Newton direction can be computed efficiently when the size of the moment … Read more