Luong Nguyen

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

    Weak sharpness and finite termination for variational inequalities on Hadamard manifolds

  • Luong Nguyen
    • Categories Nonlinear Optimization

    We first introduce the notion of weak sharpness for the solution sets of variational inequality problems (in short, VIP) on Hadamard spaces. We then study the finite convergence property of sequences generated by the inexact proximal point algorithm with different error terms for solving VIP under weak sharpness of the solution set. We also give … Read more

    Finite convergence and weak sharpness for solutions of nonsmooth variational inequalities in Hilbert spaces

  • Qamrul Hasan Ansari
  • Luong Nguyen
  • Xiaolong Qin
    • Categories Convex and Nonsmooth Optimization, Nonlinear Optimization Tags , , , , ,

    This paper deals with the study of weak sharp solutions for nonsmooth variational inequalities and finite convergence property of the proximal point method. We present several characterizations for weak sharpness of the solutions set of nonsmooth variational inequalities without using the gap functions. We show that under weak sharpness of the solutions set, the sequence … Read more