Self-adaptive iterative method for solving boundedly Lipschitz continuous and strongly monotone variational inequalities
نویسندگان
چکیده
منابع مشابه
Iterative Algorithms for Variational Inequalities Governed by Boundedly Lipschitzian and Strongly Monotone Operators
Consider the variational inequality V I(C, F ) of finding a point x∗ ∈ C satisfying the property 〈Fx∗, x − x∗〉 ≥ 0 for all x ∈ C, where C is a nonempty closed convex subset of a real Hilbert space H and F : C → H is a nonlinear mapping. If F is boundedly Lipschitzian and strongly monotone, then we prove that V I(C, F ) has a unique solution and iterative algorithms can be devised to approximate...
متن کاملHybrid Steepest-Descent Methods for Solving Variational Inequalities Governed by Boundedly Lipschitzian and Strongly Monotone Operators
Let H be a real Hilbert space and let F : H → H be a boundedly Lipschitzian and strongly monotone operator. We design three hybrid steepest descent algorithms for solving variational inequality VI C, F of finding a point x∗ ∈ C such that 〈Fx∗, x − x∗〉 ≥ 0, for all x ∈ C, where C is the set of fixed points of a strict pseudocontraction, or the set of common fixed points of finite strict pseudoco...
متن کاملSolving 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...
متن کاملGeneralized Projection Method for Non-lipschitz Multivalued Monotone Variational Inequalities
We generalize the projection method for solving strongly monotone multivalued variational inequalities when the cost operator is not necessarily Lipschitz. At each iteration at most one projection onto the constrained set is needed. When the convex constrained set is not polyhedral, we embed the proposed method in a polyhedral outer approximation procedure. This allows us to obtain the projecti...
متن کاملA modified subgradient extragradient method for solving monotone variational inequalities
In the setting of Hilbert space, a modified subgradient extragradient method is proposed for solving Lipschitz-continuous and monotone variational inequalities defined on a level set of a convex function. Our iterative process is relaxed and self-adaptive, that is, in each iteration, calculating two metric projections onto some half-spaces containing the domain is involved only and the step siz...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Inequalities and Applications
سال: 2018
ISSN: 1029-242X
DOI: 10.1186/s13660-018-1941-2