arXiv subjects

Vahid Mohebbi

Publications and source records attributed to Vahid Mohebbi.

4 recordsLinked to original sources

arXiv2021

Convergence analysis of the extragradient method for vector quasi-equilibrium problems

We study the extragradient method for solving vector quasi-equilibrium problems in Banach spaces, which generalizes the extragradient method for vector equilibrium problems and scalar quasi-equilibrium problems. We propose a regularization procedure which ensures strong convergence of the generated sequence to a solution of the vector quasi-equilibrium problem, under standard assumptions on the problem without assuming neither any monotonicity assumption on the vector valued bifunction nor any weak continuity assumption of $f$ in its arguments that in the many well-known methods have been used. Also, we show that the boundedness of the generated sequences implies that the solution set of the vector quasi-equilibrium problem is nonempty, and prove the strong convergence of the generated sequences to a solution of the problem. Finally, we give some examples of vector quasi-equilibrium problems in several Banach spaces to which our main theorem can be applied. We also present some numerical experiments.

math.OC↗

arXiv2016

On the Iterations of a Sequence of Strongly Quasi-nonexpansive Mappings with Applications

In this paper, we study $Δ$- convergence of iterations for a sequence of strongly quasi-nonexpansive mappings as well as the strong convergence of the Halpern type regularization of them in Hadamard spaces. Then, we give some their applications in iterative methods, convex and pseudo-convex minimization(proximal point algorithm), fixed point theory and equilibrium problems. The results extend several new results in the literature and some of them seem new even in Hilbert spaces.

math.FA↗

arXiv2016

Monotone and Pseudo-Monotone Equilibrium Problems in Hadamard Spaces

We study equilibrium problems in Hadamard spaces, which extend variational inequalities and many other problems in nonlinear analysis. In this paper, first we study the existence of solutions of equilibrium problems associated with pseudo-monotone bifunctions with suitable conditions on the bifunctions in Hadamard spaces. Then to approximate of an equilibrium point, we consider the proximal point algorithm for pseudo-monotone bifunctions. We prove existence of the sequence generated by the algorithm in several cases in Hadamard spaces. Next, we introduce the resolvent of a bifunction in Hadamard spaces. We prove convergence of the resolvent to an equilibrium point. We also prove $\bigtriangleup$-convergence of the sequence generated by the proximal point algorithm to an equilibrium point of the pseudo-monotone bifunction and also the strong convergence with additional assumptions on the bifunction. Finally, we study a regularization of Halpern type and prove the strong convergence of the generated sequence to an equilibrium point without any additional assumption on the pseudo-monotone bifunction. Some examples in fixed point theory and convex minimization are also presented.

math.FA↗

arXiv2016

Proximal Point Algorithm for Quasi-convex Minimization Problems in metric spaces

In this paper, the proximal point algorithm for quasi-convex minimization problem in nonpositive curvature metric spaces is studied. We prove $Δ$-convergence of the generated sequence to a critical point (which is defined in the text) of an objective convex, proper and lower semicontinuous function with at least a minimum point as well as some strong convergence results to a minimum point with some additional conditions. The results extend the recent results of the proximal point algorithm in Hadamard manifolds and CAT(0) spaces.

math.FA↗