A Note on Continuation Method for Strongly Monotone Variational Inequalities under Slater's Constraint Qualification

A Note on Globally Convergent Newton Method for Strongly Monotone Variational Inequalities

Newton’s method for solving variational inequalities is known to be locally quadratically convergent. By incorporating a line search strategy for the regularized gap function, Taji et al. (Mathematical Programming, 1993) have proposed a modification of a Newton’s method which is globally convergent and whose rate of convergence is quadratic. But the quadratic convergence has been shown only und...

A Note on a Globally Convergent Newton Method for Solving Monotone Variational Inequalities

R esum e. Il est bien connu que la m ethode de Newton, lorsqu'appliqu ee a un probl eme d'in equation variationnelle fortement monotone, converge localement vers la solution de l'in equation, et que l'ordre de convergence est quadratique. Dans cet article nous mon-trons que la direction de Newton constitue une direction de descente pour un objectif non dii erentiable et non convexe, et ceci m^ ...

Solving strongly monotone variational and quasi-variational inequalities

In this paper we develop a new and efficient method for variational inequality with Lipschitz continuous strongly monotone operator. Our analysis is based on a new strongly convex merit function. We apply a variant of the developed scheme for solving quasivariational inequality. As a result, we significantly improve the standard sufficient condition for existence and uniqueness of their solutio...

A Relaxed Extra Gradient Approximation Method of Two Inverse-Strongly Monotone Mappings for a General System of Variational Inequalities, Fixed Point and Equilibrium Problems

Necessary Optimality Conditions for Control of Strongly Monotone Variational Inequalities

In this paper we derive necessary optimality conditions involving Mordukhovich coderivatives for optimal control problems of strongly monotone variational inequalities.