A hybrid projection-proximal point algorithm for solving nonmonotone variational inequality problems

A hybrid projection-proximal point algorithm is proposed for variational inequality problems. Though the usual proximal point method and its variants require that the mapping involved be monotone, at least pseudomonotone, we assume only that the so-called Minty variational inequality has a solution, in order to ensure the global convergence. This assumption is less stringent than … Read more

An extragradient method for solving variational inequalities without monotonicity

A new extragradient projection method is devised in this paper, which does not obviously require generalized monotonicity and assumes only that the so-called dual variational inequality has a solution in order to ensure its global convergence. In particular, it applies to quasimonotone variational inequality having a nontrivial solution. Article Download View An extragradient method for … Read more

Stability of p-order metric regularity

This paper shows that $p$-order metric regularity is preserved under perturbation of H\”older continuous mapping of order $1/p$, which answers affirmatively a problem posed recently by Dontchev. Citation Technical report, Department of Mathematics, Chinese University of Hong Kong, 07/2015

A double projection method for solving variational inequalities without monotonicity

We present a double projection algorithm for solving variational inequalities without monotonicity. If the solution of dual variational inequality does exist, then the sequence produced by our method is globally convergent to a solution. Under the same assumption, the sequence produced by known methods has only a subsequence converging to a solution. Numerical experiments are … Read more