global convergence

An efficient penalty decomposition algorithm for minimization over sparse symmetric sets

  • Ahmad Mousavi
  • Morteza Kimiaei
  • Saman Babaie-Kafaki
  • Vyacheslav Kungurtsev
    • Categories Nonlinear Optimization, Nonsmooth Optimization Tags , , , ,

    This paper proposes an improved quasi-Newton penalty decomposition algorithm for the minimization of continuously differentiable functions, possibly nonconvex, over sparse symmetric sets. The method solves a sequence of penalty subproblems approximately via a two-block decomposition scheme: the first subproblem admits a closed-form solution without sparsity constraints, while the second subproblem is handled through an efficient … Read more

    An active-set method for box-constrained multiobjective optimization

  • N. S. Fazzio
  • Leandro Fonseca Prudente
  • María Laura Schuverdt
    • Categories Multi-Criteria Optimization Tags , , ,

    We propose an active-set algorithm for smooth multiobjective optimization problems subject to box constraints. The method works on one face of the feasible set at a time, treating it as a lower-dimensional region on which the problem simplifies. At each iteration, the algorithm decides whether to remain on the current face or to move to … Read more

    On constraint qualifications for lower-level sets and an augmented Lagrangian method

  • Roberto Andreani
  • Gabriel Haeser
  • Mariana da Rosa
  • Daiana O. Santos
    • Categories Nonlinear Optimization Tags , , ,

    In this paper we consider an augmented Lagrangian method with general lower-level constraints, that is, where some of the constraints are penalized while others are kept as subproblem constraints. Motivated by some recent results on optimization problems on manifolds, we present a general theory of global convergence when a feasible approximate KKT point is found … Read more

    Solving a linear program via a single unconstrained minimization

  • Adilet Otemissov
  • Alina Abdikarimova
    • Categories Linear Programming, Nonlinear Systems and Least-Squares, Unconstrained Optimization Tags , , , , ,

    This paper proposes a novel approach for solving linear programs. We reformulate a primal-dual linear program as an unconstrained minimization of a convex and twice continuously differentiable merit function. When the optimal set of the primal-dual pair is nonempty, its optimal set is equal to the optimal set of the proposed merit function. Minimizing this … Read more

    Restarting nonlinear conjugate gradient methods

  • Morteza Kimiaei
  • Saman Babaie-Kafaki
  • Vyacheslav Kungurtsev
  • Mahsa Yousefi
    • Categories Nonlinear Optimization Tags , , , ,

    In unconstrained optimization, due to the nonlinearity of the objective function or rounding errors in finite precision arithmetic, it can happen that NaN or infinite step sizes appear in the nonlinear conjugate gradient (NCG) method, or otherwise the step violates the sufficient descent condition (SDC). In this case the conjugate gradient (CG) direction must often … Read more

    A class of diagonal quasi-Newton penalty decomposition algorithms for sparse bound-constrained nonconvex optimization

  • Ahmad Mousavi
  • Morteza Kimiaei
  • Saman Babaie-Kafaki
  • Vyacheslav Kungurtsev
    • Categories Bound-constrained Optimization, Constrained Nonlinear Optimization, Quadratic Programming Tags , , ,

    This paper discusses an improved quasi-Newton penalty decomposition algorithm for the cardinality bound-constrained optimization problems whose simple bounds on the variables are assumed to be finite. Until an approximate stationary point is found, this algorithm approximates the solutions of a sequence of penalty subproblems by a two-block decomposition scheme. This scheme finds an approximate solution … Read more

    A general merit function-based global convergent framework for nonlinear optimization

  • Luís Felipe Bueno
  • Ernesto G. Birgin
  • Tiara Martini
  • Dimary Moreno López
  • Thadeu Senne
  • Thiago Siqueira Santos
    • Categories Nonlinear Optimization Tags , , , , ,

    In this paper, we revisit the convergence theory of the inexact restoration paradigm for non-linear optimization. The paper first identifies the basic elements of a globally convergent method based on merit functions. Then, the inexact restoration method that employs a two-phase iteration is introduced as a special case. A specific implementation is presented that is … Read more

    Global non-asymptotic super-linear convergence rates of regularized proximal quasi-Newton methods on non-smooth composite problems

  • Shida Wang
  • Jalal Fadili
  • Peter Ochs
    • Categories Convex and Nonsmooth Optimization, Convex Optimization, Nonsmooth Optimization Tags , ,

    In this paper, we propose two regularized proximal quasi-Newton methods with symmetric rank-1 update of the metric (SR1 quasi-Newton) to solve non-smooth convex additive composite problems. Both algorithms avoid using line search or other trust region strategies. For each of them, we prove a super-linear convergence rate that is independent of the initialization of the … Read more

    A Line Search Filter Sequential Adaptive Cubic Regularisation Algorithm for Nonlinearly Constrained Optimization

  • Yonggang Pei
  • Shaofang Song
  • Zhu Detong
    • Categories Constrained Nonlinear Optimization Tags , , , ,

    In this paper, a sequential adaptive regularization algorithm using cubics (ARC) is presented to solve nonlinear equality constrained optimization. It is motivated by the idea of handling constraints in sequential quadratic programming methods. In each iteration, we decompose the new step into the sum of the normal step and the tangential step by using composite … Read more

    A Unified Funnel Restoration SQP Algorithm

  • David Kiessling
  • Sven Leyffer
  • Charlie Vanaret
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags , , , ,

    We consider nonlinearly constrained optimization problems and discuss a generic double-loop framework consisting of four algorithmic ingredients that unifies a broad range of nonlinear optimization solvers. This framework has been implemented in the open-source solver Uno, a Swiss-army knife-like C++ optimization framework that unifies many nonlinearly constrained nonconvex optimization solvers. We illustrate the framework with … Read more