Cosmin G. Petra

Compact Representations of Structured BFGS Matrices

  • Johannes Brust
  • Sven Leyffer
  • Zichao (Wendy) Di
  • Cosmin G. Petra
    • Categories Nonlinear Optimization Tags , , , ,

    For general large-scale optimization problems compact representations exist in which recursive quasi-Newton update formulas are represented as compact matrix factorizations. For problems in which the objective function contains additional structure, so-called structured quasi-Newton methods exploit available second-derivative information and approximate unavailable second derivatives. This article develops the compact representations of two structured Broyden-Fletcher-Goldfarb-Shanno update formulas. … Read more

    A structured quasi-Newton algorithm for optimizing with incomplete Hessian information

  • Mihai Anitescu
  • Naiyuan Chiang
  • Cosmin G. Petra
    • Categories Unconstrained Optimization Tags , , ,

    We present a structured quasi-Newton algorithm for unconstrained optimization problems that have unavailable second-order derivatives or Hessian terms. We provide a formal derivation of the well-known BFGS secant update formula that approximates only the missing Hessian terms, and we propose a line-search quasi-Newton algorithm based on a modification of Wolfe conditions that converges to first-order … Read more

    On parallelizing dual decomposition in stochastic integer programming

  • Miles Lubin
  • Kipp Martin
  • Burhaneddin Sandikçi
  • Cosmin G. Petra
    • Categories Nonsmooth Optimization, Parallel Algorithms, Stochastic Programming Tags , , , , ,

    For stochastic mixed-integer programs, we revisit the dual decomposition algorithm of Car\o{}e and Schultz from a computational perspective with the aim of its parallelization. We address an important bottleneck of parallel execution by identifying a formulation that permits the parallel solution of the \textit{master} program by using structure-exploiting interior-point solvers. Our results demonstrate the potential … Read more

    Parallel distributed-memory simplex for large-scale stochastic LP problems

  • Mihai Anitescu
  • J. A. Julian Hall
  • Miles Lubin
  • Cosmin G. Petra
    • Categories Linear Programming, Parallel Algorithms, Stochastic Programming Tags , , ,

    We present a parallelization of the revised simplex method for large extensive forms of two-stage stochastic linear programming (LP) problems. These problems have been considered too large to solve with the simplex method; instead, decomposition approaches based on Benders decomposition or, more recently, interior-point methods are generally used. However, these approaches do not provide optimal … Read more

    Higher-Order Confidence Intervals for Stochastic Programming using Bootstrapping

  • Mihai Anitescu
  • Cosmin G. Petra
    • Categories Constrained Nonlinear Optimization, Stochastic Programming Tags , ,

    We study the problem of constructing confidence intervals for the optimal value of a stochastic programming problem by using bootstrapping. Bootstrapping is a resampling method used in the statistical inference of unknown parameters for which only a small number of samples can be obtained. One such parameter is the optimal value of a stochastic optimization … Read more

    Scalable Stochastic Optimization of Complex Energy Systems

  • Mihai Anitescu
  • Victor M. Zavala
  • Miles Lubin
  • Cosmin G. Petra
    • Categories Parallel Algorithms, Stochastic Programming Tags , , , ,

    We present a scalable approach and implementation for solving stochastic programming problems, with application to the optimization of complex energy systems under uncertainty. Stochastic programming is used to make decisions in the present while incorporating a model of uncertainty about future events (scenarios). These problems present serious computational difficulties as the number of scenarios becomes … Read more

    On the parallel solution of dense saddle-point linear systems arising in stochastic programming

  • Mihai Anitescu
  • Cosmin G. Petra
  • Miles Lubin
    • Categories Linear Programming, Parallel Algorithms, Stochastic Programming Tags , , ,

    We present a novel approach for solving dense saddle-point linear systems in a distributed-memory environment. This work is motivated by an application in stochastic optimization problems with recourse, but the proposed approach can be used for a large family of dense saddle-point systems, in particular those arising in convex programming. Although stochastic optimization problems have … Read more

    A preconditioning technique for Schur complement systems arising in stochastic optimization

  • Mihai Anitescu
  • Cosmin G. Petra
    • Categories Parallel Algorithms, Stochastic Programming

    Deterministic sample average approximations of stochastic programming problems with recourse are suitable for a scenario-based, treelike parallelization with interior-point methods and a Schur complement mechanism. However, the direct linear solves involving the Schur complement matrix are expensive, and adversely a ect the scalability of this approach. In this paper we propose a stochastic preconditioner to address … Read more

    A computational study of the use of an optimization-based method for simulating large multibody systems

  • Mihai Anitescu
  • Florian A. Potra
  • Bogdan Gavrea
  • Cosmin G. Petra
    • Categories Mechanical Engineering, Quadratic Programming

    The present work aims at comparing the performance of several quadratic programming (QP) solvers for simulating large-scale frictional rigid-body systems. Traditional time-stepping schemes for simulation of multibody systems are formulated as linear complementarity problems (LCPs) with copositive matrices. Such LCPs are generally solved by means of Lemketype algorithms and solvers such as the PATH solver … Read more