hadamard manifolds

VARIATIONAL INEQUALITIES GOVERNED BY STRONGLY PSEUDOMONOTONE VECTOR FIELDS ON HADAMARD MANIFOLDS

  • Nguyen Thai An
  • Luong Nguyen
  • Nguyen Thu
    • Categories Complementarity and Variational Inequalities Tags , , , , ,

    We consider variational inequalities governed by strongly pseudomonotone vec- tor fields on Hadamard manifolds. The existence and uniqueness results of the solution, linear convergence, error estimates and finite convergence for sequences generated by a mod- ified projection method for solving variational inequalities are investigated. Some examples and numerical experiments are also given to illustrate our … Read more

    Inexact scalarization proximal methods for multiobjective quasiconvex minimization on Hadamard manifold

  • Nancy Baygorrea
  • Nelson Maculan
  • Erik Alex Papa Quiroz
    • Categories Convex and Nonsmooth Optimization, Multi-Criteria Optimization, Nonsmooth Optimization Tags , , , ,

    In this paper we extend naturally the scalarization proximal point method to solve multiobjective unconstrained minimization problems, proposed by Apolinario et al.(2016), from Euclidean spaces to Hadamard manifolds for locally Lipschitz and quasiconvex vector objective functions. Moreover, we present a convergence analysis, under some mild assumptions on the multiobjective function, for two inexact variants of … Read more

    On the convergence rate of an inexact proximal point algorithm for quasiconvex minimization on Hadamard manifolds

  • Nancy Baygorrea
  • Nelson Maculan
  • Erik Alex Papa Quiroz
    • Categories Global Optimization Tags , , , , ,

    In this paper we present a rate of convergence analysis of an inexact proximal point algorithm to solve minimization problems for quasiconvex objective functions on Hadamard manifolds. We prove that under natural assumptions the sequence generated by the algorithm converges linearly or superlinearly to a critical point of the problem. ArticleDownload View PDF

    Inexact Proximal Point Methods for Quasiconvex Minimization on Hadamard Manifolds

  • Nancy Baygorrea
  • Nelson Maculan
  • Erik Alex Papa Quiroz
    • Categories Generalized Convexity/Monoticity, Global Optimization, Nonsmooth Optimization Tags , , , ,

    In this paper we present two inexact proximal point algorithms to solve minimization problems for quasiconvex objective functions on Hadamard manifolds. We prove that under natural assumptions the sequence generated by the algorithms are well defined and converge to critical points of the problem. We also present an application of the method to demand theory … Read more

    Proximal Point Method for Minimizing Quasiconvex Locally Lipschitz Functions on Hadamard Manifolds

  • Paulo Roberto Oliveira
  • Erik Alex Papa Quiroz
    • Categories Global Optimization Tags , , , ,

    In this paper we propose an extension of the proximal point method to solve minimization problems with quasiconvex locally Lipschitz objective functions on Hadamard manifolds. To reach this goal, we use the concept of Clarke subdifferential on Hadamard manifolds and assuming that the function is bounded from below, we prove the global convergence of the … Read more

    Proximal Methods with Bregman Distances to Solve VIP on Hadamard manifolds

  • Paulo Roberto Oliveira
  • Erik Alex Papa Quiroz
    • Categories Global Optimization, Global Optimization Theory Tags , , , ,

    We present an extension of the proximal point method with Bregman distances to solve Variational Inequality Problems (VIP) on Hadamard manifolds (simply connected finite dimensional Riemannian manifold with nonpositive sectional curvature). Under some natural assumption, as for example, the existence of solutions of the (VIP) and the monotonicity of the multivalued vector field, we prove … Read more

    Proximal Point Methods for Quasiconvex and Convex Functions With Bregman Distances

  • Paulo Roberto Oliveira
  • Erik Alex Papa Quiroz
    • Categories Convex Optimization, Generalized Convexity/Monoticity Tags ,

    This paper generalizes the proximal point method using Bregman distances to solve convex and quasiconvex optimization problems on noncompact Hadamard manifolds. We will proved that the sequence generated by our method is well defined and converges to an optimal solution of the problem. Also, we obtain the same convergence properties for the classical proximal method, … Read more

    Convex- and Monotone- Transformable Mathematical Programming Problems and a Proximal-Like Point Method

  • João Xavier da Cruz Neto
  • Orizon Pereira Ferreira
  • L. R. Lucambio Pérez
  • S. Z. Nemeth
    • Categories Constrained Nonlinear Optimization, Generalized Convexity/Monoticity, Global Optimization Theory Tags , ,

    The problem of finding singularities of monotone vectors fields on Hadamard manifolds will be considered and solved by extending the well-known proximal point algorithm. For monotone vector fields the algorithm will generate a well defined sequence, and for monotone vector fields with singularities it will converge to a singularity. It will be also shown how … Read more