Stephen Wright

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

Gradient Projection for Sparse Reconstruction: Application to Compressed Sensing and Other Inverse Problems

  • Mario A. T. Figueiredo
  • Stephen Wright
  • Robert Nowak
    • Categories Applications - Science and Engineering, Bound-constrained Optimization Tags ,

    Many problems in signal processing and statistical inference involve finding sparse solutions to under-determined, or ill-conditioned, linear systems of equations. A standard approach consists in minimizing an objective function which includes a quadratic (squared $\ell_2$) error term combined with a sparseness-inducing ($\ell_1$) regularization term.{\it Basis pursuit}, the {\it least absolute shrinkage and selection operator} (LASSO), … Read more

    Data Assimilation in Weather Forecasting: A Case Study in PDE-Constrained Optimization

  • M. Fisher
  • Jorge Nocedal
  • Stephen Wright
  • Y. Tremolet
    • Categories Nonlinear Optimization, Optimization of Systems modeled by PDEs Tags ,

    Variational data assimilation is used at major weather prediction centers to produce the initial conditions for 7- to 10-day weather forecasts. This technique requires the solution of a very large data-fitting problem in which the major element is a set of partial differential equations that models the evolution of the atmosphere over a time window … Read more

    An Accelerated Newton Method for Equations with Semismooth Jacobians and Nonlinear Complementarity Problems: Extended Version

  • Christina Oberlin
  • Stephen Wright
    • Categories Complementarity and Variational Inequalities, Nonlinear Systems and Least-Squares Tags , ,

    We discuss local convergence of Newton’s method to a singular solution $x^*$ of the nonlinear equations $F(x) = 0$, for $F:\R^n \rightarrow \R^n$. It is shown that an existing proof of Griewank, concerning linear convergence to a singular solution $x^*$ from a starlike domain around $x^*$ for $F$ twice Lipschitz continuously differentiable and $x^*$ satisfying … Read more

    Efficient Schemes for Robust IMRT Treatment Planning

  • Arinbjorn Olafsson
  • Stephen Wright
    • Categories Biomedical Applications, Robust Optimization Tags ,

    We use robust optimization techniques to formulate an IMRT treatment planning problem in which the dose matrices are uncertain, due to both dose calculation errors and inter-fraction positional uncertainty of tumor and organs. When the uncertainty is taken into account, the original linear programming formulation becomes a second-order cone program. We describe a novel and … Read more

    A Framework for Kernel Regularization with Applications to Protein Clustering

  • Sunduz Keles
  • Stephen Wright
  • Fan Lu
  • Grace Wahba
    • Categories Biomedical Applications, Linear, Cone and Semidefinite Programming, Statistics Tags , , , , , , ,

    We develop and apply a novel framework which is designed to extract information in the form of a positive definite kernel matrix from possibly crude, noisy, incomplete, inconsistent dissimilarity information between pairs of objects, obtainable in a variety of contexts. Any positive definite kernel defines a consistent set of distances, and the fitted kernel provides … Read more

    Elastic-Mode Algorithms for Mathematical Programs with Equilibrium Constraints: Global Convergence and Stationarity Properties

  • Mihai Anitescu
  • Paul Tseng
  • Stephen Wright
    • Categories Complementarity and Variational Inequalities, Constrained Nonlinear Optimization Tags , , , , , ,

    The elastic-mode formulation of the problem of minimizing a nonlinear function subject to equilibrium constraints has appealing local properties in that, for a finite value of the penalty parameter, local solutions satisfying first- and second-order necessary optimality conditions for the original problem are also first- and second-order points of the elastic-mode formulation. Here we study … Read more

    Active Set Identification in Nonlinear Programming

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

    Techniques that identify the active constraints at a solution of a nonlinear programming problem from a point near the solution can be a useful adjunct to nonlinear programming algorithms. They have the potential to improve the local convergence behavior of these algorithms, and in the best case can reduce an inequality constrained problem to an … Read more

    Some Properties of Regularization and Penalization Schemes for MPECs

  • Daniel Ralph
  • Stephen Wright
    • Categories Complementarity and Variational Inequalities, Constrained Nonlinear Optimization Tags , ,

    Some properties of regularized and penalized nonlinear programming formulations of mathematical programs with equilibrium constraints (MPECs) are described. The focus is on the properties of these formulations near a local solution of the MPEC at which strong stationarity and a second-order sufficient condition are satisfied. In the regularized formulations, the complementarity condition is replaced by … Read more

    An Algorithm for Degenerate Nonlinear Programming with Rapid Local Convergence

  • Stephen Wright
    • Categories Constrained Nonlinear Optimization Tags , ,

    The paper describes and analyzes an algorithmic framework for solving nonlinear programming problems in which strict complementarity conditions and constraint qualifications are not necessarily satisfied at a solution. The framework is constructed from three main algorithmic ingredients. The first is any conventional method for nonlinear programming that produces estimates of the Lagrange multipliers at each … Read more

    A Feasible Trust-Region Sequential Quadratic Programming Algorithm

  • M. J. Tenny
  • Stephen Wright
    • Categories Constrained Nonlinear Optimization Tags , ,

    An algorithm for smooth nonlinear constrained optimization problems is described, in which a sequence of feasible iterates is generated by solving a trust-region sequential quadratic programming (SQP) subproblem at each iteration, and perturbing the resulting step to retain feasibility of each iterate. By retaining feasibility, the algorithm avoids several complications of other trust-region SQP approaches: … Read more