Yunier Bello-Cruz

A Relaxed-Projection Splitting Algorithm for Variational Inequalities in Hilbert Spaces

  • Yunier Bello-Cruz
  • R. Diaz Millan
    • Categories Complementarity and Variational Inequalities, Nonlinear Optimization, Nonsmooth Optimization Tags , , , , ,

    We introduce a relaxed-projection splitting algorithm for solving variational inequalities in Hilbert spaces for the sum of nonsmooth maximal monotone operators, where the feasible set is defined by a nonlinear and nonsmooth continuous convex function inequality. In our scheme, the orthogonal projections onto the feasible set are replaced by projections onto separating hyperplanes. Furthermore, each … Read more

    A strongly convergent proximal bundle method for convex minimization in Hilbert spaces

  • Yunier Bello-Cruz
  • Welington de Oliveira
  • Wim van Ackooij
    • Categories Convex and Nonsmooth Optimization

    A key procedure in proximal bundle methods for convex minimization problems is the definition of stability centers, which are points generated by the iterative process that successfully decrease the objective function. In this paper we study a different stability-center classification rule for proximal bundle methods. We show that the proposed bundle variant has three particularly … Read more

    A direct splitting method for nonsmooth variational inequalities

  • Yunier Bello-Cruz
  • R. Diaz Millan
    • Categories Complementarity and Variational Inequalities, Convex and Nonsmooth Optimization, Nonsmooth Optimization

    We propose a direct splitting method for solving nonsmooth variational inequality problems in Hilbert spaces. The weak convergence is established, when the operator is the sum of two point-to-set and monotone operators. The proposed method is a natural extension of the incremental subgradient method for nondifferentiable optimization, which explores strongly the structure of the operator … Read more