Stephen Wright

Steve is a Professor of Computer Science at UW-Madison and a Discovery Fellow in the Wisconsin Institute for Discovery.

Nonlinear Model Predictive Control via Feasibility-Perturbed Sequential Quadratic Programming

  • J B Rawlings
  • M. J. Tenny
  • Stephen Wright
    • Categories Chemical Engineering, Constrained Nonlinear Optimization, Control Applications Tags , ,

    Model predictive control requires the solution of a sequence of continuous optimization problems that are nonlinear if a nonlinear model is used for the plant. We describe briefly a trust-region feasibility-perturbed sequential quadratic programming algorithm (developed in a companion report), then discuss its adaptation to the problems arising in nonlinear model predictive control. Computational experience … Read more

    The Empirical Behavior of Sampling Methods for Stochastic Programming

  • Jeff Linderoth
  • Alexander Shapiro
  • Stephen Wright
    • Categories Stochastic Programming Tags , ,

    We investigate the quality of solutions obtained from sample-average approximations to two-stage stochastic linear programs with recourse. We use a recently developed software tool executing on a computational grid to solve many large instances of these problems, allowing us to obtain high-quality solutions and to verify optimality and near-optimality of the computed solutions in various … Read more

    Object-Oriented Software for Quadratic Programming

  • Michael Gertz
  • Stephen Wright
    • Categories Optimization Software Design Principles, Quadratic Programming Tags , ,

    We describe the object-oriented software package OOQP for solving convex quadratic programming problems (QP). The primal-dual interior point algorithms supplied by OOQP are implemented in a way that is largely independent of the problem structure. Users may exploit problem structure by supplying linear algebra, problem data, and variable classes that are customized to their particular … Read more

    Properties of the Log-Barrier Function on Degenerate Nonlinear Programs

  • Dominique Orban
  • Stephen Wright
    • Categories Constrained Nonlinear Optimization Tags , , ,

    We examine the sequence of local minimizers of the log-barrier function for a nonlinear program near a solution at which second-order sufficient conditions and the Mangasarian-Fromovitz constraint qualifications are satisfied, but the active constraint gradients are not necessarily linearly independent. When a strict complementarity condition is satisfied, we show uniqueness of the local minimizer of … Read more

    Decomposition Algorithms for Stochastic Programming on a Computational Grid

  • Jeff Linderoth
  • Stephen Wright
    • Categories Parallel Algorithms, Stochastic Programming Tags ,

    We describe algorithms for two-stage stochastic linear programming with recourse and their implementation on a grid computing platform. In particular, we examine serial and asynchronous versions of the L-shaped method and a trust-region method. The parallel platform of choice is the dynamic, heterogeneous, opportunistic platform provided by the Condor system. The algorithms are of master-worker … Read more

    Constraint Identification and Algorithm Stabilization for Degenerate Nonlinear Programs

  • Stephen Wright
    • Categories Constrained Nonlinear Optimization Tags , , ,

    In the vicinity of a solution of a nonlinear programming problem at which both strict complementarity and linear independence of the active constraints may fail to hold, we describe a technique for distinguishing weakly active from strongly active constraints. We show that this information can be used to modify the sequential quadratic programming algorithm so … Read more

    Optimization on Computational Grids

  • Stephen Wright
    • Categories Branch and Cut Algorithms, Parallel Algorithms, Stochastic Programming Tags , , , ,

    We define the concept of a computational grid, and describe recent work in solving large and complex optimization problems on this type of platform; in particular, integer programming, the quadratic assignment problem, and stochastic programming problems. This article focuses on work conducted in the metaneos project. Citation Preprint, Mathematics and Computer Science Division, Argonne National … Read more

    On reduced QP formulations of monotone LCP problems

  • Stephen Wright
    • Categories Complementarity and Variational Inequalities, Nonlinear Optimization, Quadratic Programming Tags , ,

    Techniques for transforming convex quadratic programs (QPs) into monotone linear complementarity problems (LCPs) and vice versa are well known. We describe a class of LCPs for which a reduced QP formulation—one that has fewer constraints than the “standard” QP formulation—is available. We mention several instances of this class, including the known case in which the … Read more

    Warm start strategies in interior-point methods for linear programming

  • Stephen Wright
  • E. Alper Yildirim
    • Categories Linear Programming, Linear, Cone and Semidefinite Programming Tags , , ,

    We study the situation in which, having solved a linear program with an interior-point method, we are presented with a new problem instance whose data is slightly perturbed from the original. We describe strategies for recovering a “warm-start” point for the perturbed problem instance from the iterates of the original problem instance. We obtain worst-case … Read more