large-scale optimization

On-Line Economic Optimization of Energy Systems Using Weather Forecast Information

  • Mihai Anitescu
  • Emil M. Constantinescu
  • Victor M. Zavala
  • Theodore Krause
    • Categories Chemical Engineering, Control Applications, Stochastic Programming Tags , , , , ,

    We establish an on-line optimization framework to exploit weather forecast information in the operation of energy systems. We argue that anticipating the weather conditions can lead to more proactive and cost-effective operations. The framework is based on the solution of a stochastic dynamic real-time optimization (D-RTO) problem incorporating forecasts generated from a state-of-the-art weather prediction … Read more

    An Interior-Point Algorithm for Large-Scale Nonlinear Optimization with Inexact Step Computations

  • Frank E. Curtis
  • Olaf Schenk
    • Categories Nonlinear Optimization, Optimization of Systems modeled by PDEs Tags , , , , , ,

    We present a line-search algorithm for large-scale continuous optimization. The algorithm is matrix-free in that it does not require the factorization of derivative matrices. Instead, it uses iterative linear system solvers. Inexact step computations are supported in order to save computational expense during each iteration. The algorithm is an interior-point approach derived from an inexact … Read more

    A Fast Moving Horizon Estimation Algorithm Based on Nonlinear Programming Sensitivity

  • Lorenz T. Biegler
  • Carl D. Laird
  • Victor M. Zavala
    • Categories Control Applications, Nonlinear Optimization, Systems governed by Differential Equations Optimization Tags , , , ,

    Moving Horizon Estimation (MHE) is an efficient optimization-based strategy for state estimation. Despite the attractiveness of this method, its application in industrial settings has been rather limited. This has been mainly due to the difficulty to solve, in real-time, the associated dynamic optimization problems. In this work, a fast MHE algorithm able to overcome this … Read more

    Approximate Level Method

  • Peter Richtarik
    • Categories Convex and Nonsmooth Optimization, Convex Optimization, Nonsmooth Optimization Tags , , , ,

    In this paper we propose and analyze a variant of the level method [4], which is an algorithm for minimizing nonsmooth convex functions. The main work per iteration is spent on 1) minimizing a piecewise-linear model of the objective function and on 2) projecting onto the intersection of the feasible region and a polyhedron arising … Read more

    A Matrix-free Algorithm for Equality Constrained Optimization Problems with Rank-deficient Jacobians

  • Frank E. Curtis
  • Jorge Nocedal
  • Andreas Wächter
    • Categories Constrained Nonlinear Optimization, Infinite Dimensional Optimization Tags , , , , ,

    We present a line search algorithm for large-scale constrained optimization that is robust and efficient even for problems with (nearly) rank-deficient Jacobian matrices. The method is matrix-free (i.e., it does not require explicit storage or factorizations of derivative matrices), allows for inexact step computations, and is applicable for nonconvex problems. The main components of the … Read more

    On mutual impact of numerical linear algebra and large-scale optimization with focus on interior point methods

  • Marco D'Apuzzo
  • Valentina De Simone
  • Daniela di Serafino
    • Categories Constrained Nonlinear Optimization Tags , , , , ,

    The solution of KKT systems is ubiquitous in optimization methods and often dominates the computation time, especially when large-scale problems are considered. Thus, the effective implementation of such methods is highly dependent on the availability of effective linear algebra algorithms and software, that are able, in turn, to take into account specific needs of optimization. … Read more

    Primal interior point method for minimization of generalized minimax functions

  • Ladislav Lukšan
  • Ctirad Matonoha
  • Jan Vlček
    • Categories Nonlinear Optimization, Nonsmooth Optimization, Unconstrained Optimization Tags , , , , , , , ,

    In this report, we propose a primal interior-point method for large sparse generalized minimax optimization. After a short introduction, where the problem is stated, we introduce the basic equations of the Newton method applied to the KKT conditions and propose a primal interior-point method. Next we describe the basic algorithm and give more details concerning … Read more

    An Inexact Newton Method for Nonconvex Equality Constrained Optimization

  • Richard H. Byrd
  • Frank E. Curtis
  • Jorge Nocedal
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization, Systems governed by Differential Equations Optimization Tags , , , ,

    We present a matrix-free line search algorithm for large-scale equality constrained optimization that allows for inexact step computations. For strictly convex problems, the method reduces to the inexact sequential quadratic programming approach proposed by Byrd et al. [SIAM J. Optim. 19(1) 351–369, 2008]. For nonconvex problems, the methodology developed in this paper allows for the … Read more

    Exploiting separability in large-scale linear support vector machine training

  • Jacek Gondzio
  • Kristian Woodsend
    • Categories Data-Mining, Quadratic Programming Tags , , ,

    Linear support vector machine training can be represented as a large quadratic program. We present an efficient and numerically stable algorithm for this problem using interior point methods, which requires only O(n) operations per iteration. Through exploiting the separability of the Hessian, we provide a unified approach, from an optimization perspective, to 1-norm classification, 2-norm … Read more

    A 2-BFGS updating in a trust region framework

  • Marianna S. Apostolopoulou
  • Panagiotis Pintelas
  • Dimitris G. Sotiropoulos
    • Categories Nonlinear Optimization, Unconstrained Optimization Tags , , , ,

    We present a new matrix-free method for the trust region subproblem, assuming that the approximate Hessian is updated by the limited memory BFGS formula with m = 2. The resulting updating scheme, called 2-BFGS, give us the ability to determine via simple formulas the eigenvalues of the resulting approximation. Thus, at each iteration, we can … Read more