constrained optimization

A Sequential Quadratic Programming Algorithm for Nonconvex, Nonsmooth Constrained Optimization

  • Frank E. Curtis
  • Michael L. Overton
    • Categories Constrained Nonlinear Optimization, Nonsmooth Optimization Tags , , , , ,

    We consider optimization problems with objective and constraint functions that may be nonconvex and nonsmooth. Problems of this type arise in important applications, many having solutions at points of nondifferentiability of the problem functions. We present a line search algorithm for situations when the objective and constraint functions are locally Lipschitz and continuously differentiable on … Read more

    Algorithm 909: NOMAD: Nonlinear Optimization with the MADS algorithm

  • Sébastien Le Digabel
    • Categories Applications - OR and Management Sciences, Optimization Software and Modeling Systems Tags , , , ,

    NOMAD is software that implements the MADS algorithm (Mesh Adaptive Direct Search) for black-box optimization under general nonlinear constraints. Blackbox optimization is about optimizing functions that are usually given as costly programs with no derivative information and no function values returned for a significant number of calls attempted. NOMAD is designed for such problems and … 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

    Identifying Activity

  • Adrian Lewis
  • Stephen Wright
    • Categories Constrained Nonlinear Optimization, Nonsmooth Optimization Tags , , , ,

    Identification of active constraints in constrained optimization is of interest from both practical and theoretical viewpoints, as it holds the promise of reducing an inequality-constrained problem to an equality-constrained problem, in a neighborhood of a solution. We study this issue in the more general setting of composite nonsmooth minimization, in which the objective is a … 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

    Duality-Based Algorithms for Total-Variation-Regularized Image Restoration

  • Tony F. Chan
  • Stephen Wright
  • Mingqiang Zhu
    • Categories Basic Sciences Applications, Convex Optimization Tags , ,

    Image restoration models based on total variation (TV) have become popular since their introduction by Rudin, Osher, and Fatemi (ROF) in 1992. The dual formulation of this model has a quadratic objective with separable constraints, making projections onto the feasible set easy to compute. This paper proposes application of gradient projection (GP) algorithms to the … Read more

    A stochastic algorithm for function minimization

  • Su Dongcai
  • Dong Junwei
  • Zheng Zuduo
    • Categories Constrained Nonlinear Optimization, Stochastic Approaches, Unconstrained Optimization Tags , ,

    Focusing on what an optimization problem may comply with, the so-called convergence conditions have been proposed and sequentially a stochastic optimization algorithm named as DSZ algorithm is presented in order to deal with both unconstrained and constrained optimizations. Its principle is discussed in the theoretical model of DSZ algorithm, from which we present a practical … 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

    OrthoMADS: A deterministic MADS instance with orthogonal directions

  • Mark A. Abramson
  • Charles Audet
  • John E. Dennis, Jr.
  • Sébastien Le Digabel
    • Categories Applications - OR and Management Sciences, Nonsmooth Optimization Tags , , , ,

    he purpose of this paper is to introduce a new way of choosing directions for the mesh adaptive direct search (Mads) class of algorithms. The advantages of this new OrthoMads instantiation of Mads are that the polling directions are chosen deterministically, ensuring that the results of a given run are repeatable, and that they are … Read more