Jorge Nocedal

Subspace accelerated matrix splitting algorithms for bound-constrained quadratic programming and linear complementarity problems

  • Liming Feng
  • Jorge Nocedal
  • Daniel P. Robinson
  • Jong-Shi Pang
    • Categories Bound-constrained Optimization, Finance and Economics Tags , , , , , , ,

    This paper studies the solution of two problems—bound-constrained quadratic programs and linear complementarity problems—by two-phase methods that consist of an active set prediction phase and a subspace phase. The algorithms enjoy favorable convergence properties under weaker assumptions than those assumed for other methods in the literature. The active set prediction phase employs matrix splitting iterations … Read more

    An Implementation of an Algorithm for Nonlinear Programming Based on Piecewise Linear Models

  • Richard H. Byrd
  • Jorge Nocedal
  • Richard A. Waltz
  • Yuchen Wu
    • Categories Constrained Nonlinear Optimization Tags ,

    This is a progress report on an implementation of the active-set method for nonlinear programming proposed in [6] that employs piecewise linear models in the active-set prediction phase. The motivation for this work is to develop an algorithm that is capable of solving large-scale problems, including those with a large reduced space. Unlike SQP methods, … Read more

    On the Use of Stochastic Hessian Information in Unconstrained Optimization

  • Richard H. Byrd
  • Gillian M Chin
  • Jorge Nocedal
  • Will Neveitt
    • Categories Nonlinear Optimization, Stochastic Programming Tags , ,

    This paper describes how to incorporate stochastic curvature information in a Newton- CG method and in a limited memory quasi-Newton method for large scale optimization. The motivation for this work stems from statistical learning and stochastic optimization applications in which the objective function is the sum of a very large number of loss terms, and … Read more

    On the Solution of Complementarity Problems Arising in American Options Pricing

  • Liming Feng
  • V. Linetsky
  • Jose Luis Morales
  • Jorge Nocedal
    • Categories Applications - OR and Management Sciences, Complementarity and Variational Inequalities, Finance and Economics Tags , ,

    In the Black-Scholes-Merton model, as well as in more general stochastic models in finance, the price of an American option solves a system of partial differential variational inequalities. When these inequalities are discretized, one obtains a linear complementarity problem that must be solved at each time step. This paper presents an algorithm for the solution … Read more

    A Line Search Exact Penalty Method Using Steering Rules

  • Richard H. Byrd
  • Gabriel Lopez-Calva
  • Jorge Nocedal
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags , ,

    Line search algorithms for nonlinear programming must include safeguards to enjoy global convergence properties. This paper describes an exact penalization approach that extends the class of problems that can be solved with line search SQP methods. In the new algorithm, the penalty parameter is adjusted at every iteration to ensure sufficient progress in linear feasibility … Read more

    A Sequential Quadratic Programming Algorithm with an Additional Equality Constrained Phase

  • Jose Luis Morales
  • Jorge Nocedal
  • Yuchen Wu
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags ,

    A sequential quadratic programming (SQP) method is presented that aims to overcome some of the drawbacks of contemporary SQP methods. It avoids the difficulties associated with indefinite quadratic programming subproblems by defining this subproblem to be always convex. The novel feature of the approach is the addition of an equality constrained phase that promotes fast … Read more

    Infeasibility Detection and SQP Methods for Nonlinear Optimization

  • Richard H. Byrd
  • Frank E. Curtis
  • Jorge Nocedal
    • Categories Nonlinear Optimization Tags , ,

    This paper addresses the need for nonlinear programming algorithms that provide fast local convergence guarantees regardless of whether a problem is feasible or infeasible. We present a sequential quadratic programming method derived from an exact penalty approach that adjusts the penalty parameter automatically, when appropriate, to emphasize feasibility over optimality. The superlinear convergence of such … 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 the Geometry Phase in Model-Based Algorithms for Derivative-Free Optimization

  • Giovanni Fasano
  • Jose Luis Morales
  • Jorge Nocedal
    • Categories Nonlinear Optimization Tags ,

    A numerical study of model-based methods for derivative-free optimization is presented. These methods typically include a geometry phase whose goal is to ensure the adequacy of the interpolation set. The paper studies the performance of an algorithm that dispenses with the geometry phase altogether (and therefore does not attempt to control the position of the … 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