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This article proposes two general inertial algorithms with line-search process for finding a solution of a variational inequality problem with fixed-point constraints via a subgradient-extragradient approach. Common solution theorems are obtained in Hilbert spaces. [ABSTRACT FROM AUTHOR]

In this paper, the local weak Pareto optimality conditions for nonsmooth vector optimization problems are presented on Hadamard manifolds. Some convergence results of the parallel proximal point algorithms for finding a solution of vector optimization problems are established. [ABSTRACT FROM AUTHOR]

In this article, we consider a monotone variational inequality with variational inequality constraint over the set of fixed points of a nonexpansive mapping, which is called a triple-hierarchical variational inequality (THVI). A relaxed hybrid steepest-descent method with variable parameters is introduced for solving the THVI. Strong convergence of the method to a unique solution of the THVI is studied under certain assumptions. We also investigate another monotone variational inequality with the variational inequality constraint over the set of common fixed points of a finite family of nonexpansive mappings, and present an iterative algorithm for solving such kind of problems. It is proven that under mild conditions the sequence generated by the proposed algorithm converges strongly to a unique solution of later problem. [ABSTRACT FROM AUTHOR]

Let E be a uniformly convex and uniformly smooth Banach space with the dual E* and let T : E → 2E* be a maximal monotone operator. By using the technique of resolvent operators and by using modified Ishikawa iteration and modified Halpern iteration for relatively non-expansive mappings, we suggest and analyse two iterative algorithms for finding an element x ∈ E such that 0 ∈ T(x). Strong convergence theorems for such iterative algorithms are proved. The ideas of these algorithms are applied to solve the problem of finding a minimizer of a convex function on E. [ABSTRACT FROM AUTHOR]

In this article, we introduce two hybrid proximal-type algorithms and two hybrid shrinking projection algorithms by using the hybrid proximal-type method and the hybrid shrinking projection method, respectively, for finding a common element of the set of solutions of an equilibrium problem, the set of fixed points of a relatively nonexpansive mapping, and the set of solutions to the equation 0 ∈ Tx for a maximal monotone operator T defined on a uniformly smooth and uniformly convex Banach space. The strong convergence of the sequences generated by the proposed algorithms is established. Our results improve and generalize several known results in the literature. [ABSTRACT FROM AUTHOR]

In this article, we introduce and study a class of generalized mixed vector equilibrium problems for multifunctions, which includes as special cases a number of generalized vector variational inequalities, generalized vector variational-like inequalities and generalized vector equilibrium problems. We first establish a new vector version of Minty's lemma, and then prove an existence theorem of solutions for the generalized mixed vector equilibrium problems by using this result. Furthermore, this existence theorem is applied to obtain a new existence result of solutions for a class of generalized vector variational-like inequalities. [ABSTRACT FROM AUTHOR]