global convergence

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 … 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

    A Subspace Minimization Barzilai-Borwein Method for Multiobjective Optimization Problems

  • Jian Chen
    • Categories Multi-Criteria Optimization Tags , , ,

    Nonlinear conjugate gradient methods have recently garnered significant attention within the multiobjective optimization community. These methods aim to maintain consistency in conjugate parameters with their single-objective optimization counterparts. However, the preservation of the attractive conjugate property of search directions remains uncertain, even for quadratic cases, in multiobjective conjugate gradient methods. This loss of interpretability of … Read more

    Strong global convergence properties of algorithms for nonlinear symmetric cone programming

  • Roberto Andreani
  • Gabriel Haeser
  • Alberto Ramos
  • Daiana O. Santos
  • Leonardo D. Secchin
  • Ariel Serranoni
    • Categories Cone Programming, Second-Order Cone Programming, Semi-definite Programming Tags , , ,

    Sequential optimality conditions have played a major role in proving strong global convergence properties of numerical algorithms for many classes of optimization problems. In particular, the way complementarity is dealt is fundamental to achieve a strong condition. Typically, one uses the inner product structure to measure complementarity, which gives a very general approach to a … Read more

    Full-low evaluation methods for bound and linearly constrained derivative-free optimization

  • ClĂ©ment W. Royer
  • Oumaima Sohab
  • Luis Nunes Vicente
    • Categories Bound-constrained Optimization, Nonlinear Optimization Tags , , ,

    Derivative-free optimization (DFO) consists in finding the best value of an objective function without relying on derivatives. To tackle such problems, one may build approximate derivatives, using for instance finite-difference estimates. One may also design algorithmic strategies that perform space exploration and seek improvement over the current point. The first type of strategy often provides … Read more

    Global convergence of a BFGS-type algorithm for nonconvex multiobjective optimization problems

  • Leandro Fonseca Prudente
  • D. R. Souza
    • Categories Multi-Criteria Optimization Tags , , , , , ,

    We propose a modified BFGS algorithm for multiobjective optimization problems with global convergence, even in the absence of convexity assumptions on the objective functions. Furthermore, we establish the superlinear convergence of the method under usual conditions. Our approach employs Wolfe step sizes and ensures that the Hessian approximations are updated and corrected at each iteration … Read more

    Constraint qualifications and strong global convergence properties of an augmented Lagrangian method on Riemannian manifolds

  • Roberto Andreani
  • Kelvin Rodrigues Couto
  • Orizon Pereira Ferreira
  • Gabriel Haeser
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags , , ,

    In the past years, augmented Lagrangian methods have been successfully applied to several classes of non-convex optimization problems, inspiring new developments in both theory and practice. In this paper we bring most of these recent developments from nonlinear programming to the context of optimization on Riemannian manifolds, including equality and inequality constraints. Many research have … Read more

    Polyhedral Newton-min algorithms for complementarity problems

  • Jean-Pierre Dussault
  • Mathieu Frappier
  • Jean Charles Gilbert
    • Categories Complementarity and Variational Inequalities Tags , , , , , , , ,

    The semismooth Newton method is a very efficient approach for computing a zero of a large class of nonsmooth equations. When the initial iterate is sufficiently close to a regular zero and the function is strongly semismooth, the generated sequence converges quadratically to that zero, while the iteration only requires to solve a linear system. … Read more

    A worst-case complexity analysis for Riemannian non-monotone line-search methods

  • Harry Oviedo
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags , , ,

    In this paper we deal with non-monotone line-search methods to minimize a smooth cost function on a Riemannian manifold. In particular, we study the number of iterations necessary for this class of algorithms to obtain e-approximated stationary points. Specifically, we prove that under a regularity Lipschitz-type condition on the pullbacks of the cost function to … Read more