39 research outputs found
Weak convergence for variational inequalities with inertial-type method
Weak convergence of inertial iterative method for solving variational inequalities is the focus of this paper. The cost function is assumed to be non-Lipschitz and monotone. We propose a projection-type method with inertial terms and give weak convergence analysis under appropriate conditions. Some test results are performed and compared with relevant methods in the literature to show the efficiency and advantages given by our proposed methods
A new inertial condition on the subgradient extragradient method for solving pseudomonotone equilibrium problem
In this paper we study the pseudomonotone equilibrium problem. We consider a
new inertial condition for the subgradient extragradient method with
self-adaptive step size for approximating a solution of the equilibrium problem
in a real Hilbert space. Our proposed method contains inertial factor with new
conditions that only depend on the iteration coefficient. We obtain a weak
convergence result of the proposed method under weaker conditions on the
inertial factor than many existing conditions in the literature. Finally, we
present some numerical experiments for our proposed method in comparison with
existing methods in the literature. Our result improves, extends and
generalizes several existing results in the literature
Modified inertial subgradient extragradient algorithms for generalized equilibria systems with constraints of variational inequalities and fixed points
In this research, we studied modified inertial composite subgradient extragradient implicit rules for finding solutions of a system of generalized equilibrium problems with a common fixed-point problem and pseudomonotone variational inequality constraints. The suggested methods consisted of an inertial iterative algorithm, a hybrid deepest-descent technique, and a subgradient extragradient method. We proved that the constructed algorithms converge to a solution of the considered problem, which also solved some hierarchical variational inequality
An Interior Projected-Like Subgradient Method for Mixed Variational Inequalities
An interior projected-like subgradient method for mixed variational inequalities is proposed in finite dimensional spaces, which is based on using non-Euclidean projection-like operator. Under suitable assumptions, we prove that the sequence generated by the proposed method converges to a solution of the mixed variational inequality. Moreover, we give the convergence estimate of the method. The results presented in this paper generalize some recent results given in the literatures
Self-adaptive inertial algorithms for approximating solutions of split feasilbility, monotone inclusion, variational inequality and fixed point problems.
Masters Degree. University of KwaZulu-Natal, Durban.In this dissertation, we introduce a self-adaptive hybrid inertial algorithm for approximating
a solution of split feasibility problem which also solves a monotone inclusion problem
and a fixed point problem in p-uniformly convex and uniformly smooth Banach spaces.
We prove a strong convergence theorem for the sequence generated by our algorithm which
does not require a prior knowledge of the norm of the bounded linear operator. Numerical
examples are given to compare the computational performance of our algorithm with other
existing algorithms.
Moreover, we present a new iterative algorithm of inertial form for solving Monotone Inclusion
Problem (MIP) and common Fixed Point Problem (FPP) of a finite family of
demimetric mappings in a real Hilbert space. Motivated by the Armijo line search technique,
we incorporate the inertial technique to accelerate the convergence of the proposed
method. Under standard and mild assumptions of monotonicity and Lipschitz continuity
of the MIP associated mappings, we establish the strong convergence of the iterative
algorithm. Some numerical examples are presented to illustrate the performance of our
method as well as comparing it with the non-inertial version and some related methods in
the literature.
Furthermore, we propose a new modified self-adaptive inertial subgradient extragradient
algorithm in which the two projections are made onto some half spaces. Moreover, under
mild conditions, we obtain a strong convergence of the sequence generated by our proposed
algorithm for approximating a common solution of variational inequality problems
and common fixed points of a finite family of demicontractive mappings in a real Hilbert
space. The main advantages of our algorithm are: strong convergence result obtained
without prior knowledge of the Lipschitz constant of the the related monotone operator,
the two projections made onto some half-spaces and the inertial technique which speeds
up rate of convergence. Finally, we present an application and a numerical example to
illustrate the usefulness and applicability of our algorithm
Proximal algorithms for a class of mixed equilibrium problems
Version of RecordPublishe