Constrained Nonlinear Optimization

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

    Necessary optimality conditions in pessimistic bilevel programming

  • Stephan Dempe
  • Boris S. Mordukhovich
  • Alain Zemkoho
    • Categories Constrained Nonlinear Optimization, Nonsmooth Optimization

    This paper is devoted to the so-called pessimistic version of bilevel programming programs. Minimization problems of this type are challenging to handle partly because the corresponding value functions are often merely upper (while not lower) semicontinuous. Employing advanced tools of variational analysis and generalized differentiation, we provide rather general frameworks ensuring the Lipschitz continuity of … Read more

    The Lagrange method and SAO with bounds on the dual variables

  • M.J.D. Powell
    • Categories Constrained Nonlinear Optimization

    We consider the general nonlinear programming problem with equality and inequality constraints when the variables x are confined to a compact set. We regard the Lagrange multipliers as dual variables lambda, those of the inequalities being nonnegative. For each lambda, we let phi(lambda) be the least value of the Lagrange function, which occurs at x=x(lambda), … Read more

    Inexact Restoration method for Derivative-Free Optimization with smooth constraints

  • Luís Felipe Bueno
  • A. Friedlander
  • José Mario Martínez
  • Francisco N. C. Sobral
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization, Optimization Software and Modeling Systems Tags , , ,

    A new method is introduced for solving constrained optimization problems in which the derivatives of the constraints are available but the derivatives of the objective function are not. The method is based on the Inexact Restoration framework, by means of which each iteration is divided in two phases. In the first phase one considers only … Read more

    New optimality conditions for the semivectorial bilevel optimization problem

  • Stephan Dempe
  • Alain Zemkoho
  • Nazih Gadhi
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization, Nonsmooth Optimization Tags , , , ,

    The paper is concerned with the optimistic formulation of a bilevel optimization problem with multiobjective lower-level problem. Considering the scalarization approach for the multiobjective program, we transform our problem into a scalar-objective optimization problem with inequality constraints by means of the well-known optimal value reformulation. Completely detailed rst-order necessary optimality conditions are then derived in … Read more