large-scale optimization

Computational and Economic Limitations of Dispatch Operations in the Next-Generation Power Grid

  • Audun Botterud
  • Emil M. Constantinescu
  • Victor M. Zavala
  • Jianhui Wang
    • Categories Dynamic Programming, Linear Programming, Production and Logistics Tags , , , , ,

    We study the interactions between computational and economic performance of dispatch operations under highly dynamic environments. In particular, we discuss the need for extending the forecast horizon of the dispatch formulation in order to anticipate steep variations of renewable power and highly elastic loads. We present computational strategies to solve the increasingly larger optimization problems … Read more

    A Penalty-Interior-Point Algorithm for Nonlinear Constrained Optimization

  • Frank E. Curtis
    • Categories Constrained Nonlinear Optimization Tags , , , , , ,

    Penalty and interior-point methods for nonlinear optimization problems have enjoyed great successes for decades. Penalty methods have proved to be effective for a variety of problem classes due to their regularization effects on the constraints. They have also been shown to allow for rapid infeasibility detection. Interior-point methods have become the workhorse in large-scale optimization … Read more

    A Non-monotonic Method for Large-scale Nonnegative Least Squares

  • Inderjit S. Dhillon
  • Dongmin Kim
  • Suvrit Sra
    • Categories Basic Sciences Applications, Bound-constrained Optimization, Nonlinear Systems and Least-Squares Tags , , , , , ,

    We present a new algorithm for nonnegative least-squares (NNLS). Our algorithm extends the unconstrained quadratic optimization algorithm of Barzilai and Borwein (BB) (J. Barzilai and J. M. Borwein; Two-Point Step Size Gradient Methods. IMA J. Numerical Analysis; 1988.) to handle nonnegativity constraints. Our extension diff ers in several basic aspects from other constrained BB variants. The … Read more

    Alternating Direction Methods for Sparse Covariance Selection

  • Xiao-Ming Yuan
    • Categories Convex and Nonsmooth Optimization Tags , , , ,

    The mathematical model of the widely-used sparse covariance selection problem (SCSP) is an NP-hard combinatorial problem, whereas it can be well approximately by a convex relaxation problem whose maximum likelihood estimation is penalized by the $L_1$ norm. This convex relaxation problem, however, is still numerically challenging, especially for large-scale cases. Recently, some efficient first-order methods … Read more

    A new LP algorithm for precedence constrained production scheduling

  • Daniel Bienstock
  • Mark Zuckerberg
    • Categories Combinatorial Optimization, Integer Programming, Linear, Cone and Semidefinite Programming Tags , ,

    We present a number of new algorithmic ideas for solving LP relaxations of extremely large precedence constrained production scheduling problems. These ideas are used to develop an implementation that is tested on a variety of real-life, large scale instances; yielding optimal solutions in very practicable CPU time. Citation Unpublished. Columbia University, BHP Billiton, August 2009. … Read more

    A practical method for solving large-scale TRS

  • Marianna S. Apostolopoulou
  • C.A. Botsaris
  • Panagiotis Pintelas
  • Dimitris G. Sotiropoulos
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization, Quadratic Programming Tags , , , , ,

    We present a nearly-exact method for the large scale trust region subproblem (TRS) based on the properties of the minimal-memory BFGS method. Our study in concentrated in the case where the initial BFGS matrix can be any scaled identity matrix. The proposed method is a variant of the Mor\'{e}-Sorensen method that exploits the eigenstructure of … Read more

    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