Projected subgradient method for non - Lipschitz set - valued mixed variational inequalities
نویسنده
چکیده
A projected subgradient method for solving a class of set-valued mixed variational inequalities (SMVIs) is proposed when the mapping is not necessarily Lipschitz. Under some suitable conditions, it can be proven that the sequence generated by the method can strongly converge to the unique solution to the problem in the Hilbert spaces.
منابع مشابه
Strong Convergence of the Halpern Subgradient Extragradient Method for Solving Variational Inequalities in Hilbert Spaces
In this paper, we combine the subgradient extragradient method with the Halpern method for finding a solution of a variational inequality involving a monotone Lipschitz mapping in Banach spaces. By using the generalized projection operator and the Lyapunov functional introduced by Alber, we prove a strong convergence theorem. We also consider the problem of finding a common element of the set o...
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 کاملConvergence Rates for Deterministic and Stochastic Subgradient Methods Without Lipschitz Continuity
We extend the classic convergence rate theory for subgradient methods to apply to non-Lipschitz functions. For the deterministic projected subgradient method, we present a global O(1/ √ T ) convergence rate for any convex function which is locally Lipschitz around its minimizers. This approach is based on Shor’s classic subgradient analysis and implies generalizations of the standard convergenc...
متن کاملNew Approximate Schemes for Generalized General Set-valued Mixed Quasi Variational Inequalities
In this paper, we suggest and consider a class of new three-step approximation schemes for generalized general set-valued mixed quasi variational inequalities. We also consider and analyze a new class of extragradienttype methods for solving generalized set-valued variational inequalities. The proposed methods include several new and known methods as special cases. Our results present a signifi...
متن کاملProjected Reflected Gradient Methods for Monotone Variational Inequalities
This paper is concerned with some new projection methods for solving variational inequality problems with monotone and Lipschitz-continuous mapping in Hilbert space. First, we propose the projected reflected gradient algorithm with a constant stepsize. It is similar to the projected gradient method, namely, the method requires only one projection onto the feasible set and only one value of the ...
متن کامل