Constrained Nonlinear Optimization

Proximal-like contraction methods for monotone variational inequalities in a unified framework

  • Bingsheng He
  • Lizhi Liao
  • Xiang Wang
    • Categories Complementarity and Variational Inequalities, Constrained Nonlinear Optimization, Convex Optimization Tags , ,

    Approximate proximal point algorithms (abbreviated as APPAs) are classical approaches for convex optimization problems and monotone variational inequalities. To solve the subproblems of these algorithms, the projection method takes the iteration in form of $u^{k+1} = P_{\Omega}[u^k-\alpha_k d^k]$. Interestingly, many of them can be paired such that $%\exists \tilde{u}^k, \tilde{u}^k = P_{\Omega}[u^k – \beta_kF(v^k)] = … Read more

    Proximal Methods for Nonlinear Programming: Double Regularization and Inexact Subproblems

  • Jonathan Eckstein
  • Paulo J. S. Silva
    • Categories Constrained Nonlinear Optimization, Convex Optimization Tags , ,

    This paper describes the first phase of a project attempting to construct an efficient general-purpose nonlinear optimizer using an augmented Lagrangian outer loop with a relative error criterion, and an inner loop employing a state-of-the art conjugate gradient solver. The outer loop can also employ double regularized proximal kernels, a fairly recent theoretical development that … Read more

    A second derivative SQP method: theoretical issues

  • Nicholas I. M. Gould
  • Daniel P. Robinson
    • Categories Constrained Nonlinear Optimization Tags , , , ,

    Sequential quadratic programming (SQP) methods form a class of highly efficient algorithms for solving nonlinearly constrained optimization problems. Although second derivative information may often be calculated, there is little practical theory that justifies exact-Hessian SQP methods. In particular, the resulting quadratic programming (QP) subproblems are often nonconvex, and thus finding their global solutions may be … Read more

    Necessary conditions for local optimality in d.c. programming

  • Immanuel M. Bomze
  • Claude Lemaréchal
    • Categories Constrained Nonlinear Optimization, Unconstrained Optimization

    Using $\eps$-subdifferential calculus for difference-of-convex (d.c.) programming, D\”ur proposed a condition sufficient for local optimality, and showed that this condition is not necessary in general. Here it is proved that whenever the convex part is strongly convex, this condition is also necessary. Strong convexity can always be ensured by changing the given d.c. decomposition slightly. … Read more

    A globally convergent primal-dual interior-point filter method for nonlinear programming: new filter optimality measures and computational results

  • R. Silva
  • Michael Ulbrich
  • Stefan Ulbrich
  • Luis Nunes Vicente
    • Categories Constrained Nonlinear Optimization, Optimization Software and Modeling Systems, Quadratic Programming Tags , , , ,

    In this paper we modify the original primal-dual interior-point filter method proposed in [18] for the solution of nonlinear programming problems. We introduce two new optimality filter entries based on the objective function, and thus better suited for the purposes of minimization, and propose conditions for using inexact Hessians. We show that the global convergence … Read more

    PSwarm: A Hybrid Solver for Linearly Constrained Global Derivative-Free Optimization

  • A. Ismael F. Vaz
  • Luis Nunes Vicente
    • Categories Applications - Science and Engineering, Constrained Nonlinear Optimization, Global Optimization Tags , , , , , , ,

    PSwarm was developed originally for the global optimization of functions without derivatives and where the variables are within upper and lower bounds. The underlying algorithm used is a pattern search method, more specifically a coordinate search method, which guarantees convergence to stationary points from arbitrary starting points. In the (optional) search step of coordinate search, … Read more

    Group sparsity via linear-time projection

  • Michael P. Friedlander
  • Kevin Murphy
  • Mark Schmidt
  • Ewout van den Berg
    • Categories Constrained Nonlinear Optimization

    We present an efficient spectral projected-gradient algorithm for optimization subject to a group one-norm constraint. Our approach is based on a novel linear-time algorithm for Euclidean projection onto the one- and group one-norm constraints. Numerical experiments on large data sets suggest that the proposed method is substantially more efficient and scalable than existing methods. CitationTechnical … 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 SECOND DERIVATIVE SQP METHOD WITH IMPOSED DESCENT

  • Nicholas I. M. Gould
  • Daniel P. Robinson
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags , , , ,

    Sequential quadratic programming (SQP) methods form a class of highly efficient algorithms for solving nonlinearly constrained optimization problems. Although second derivative information may often be calculated, there is little practical theory that justifies exact-Hessian SQP methods. In particular, the resulting quadratic programming (QP) subproblems are often nonconvex, and thus finding their global solutions may be … 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