[PDF] Top 20 Iterative methods for solving a class of monotone variational inequality problems with applications

... The purpose of this paper is to answer the question mentioned above. In order to re- alize this objective, we first establish a new existence and uniqueness theorem for MVIP (.), where F : C → H is a hemicontinuous and ... See full document

... our iterative method to solve some specific practical numerical cal- culation ...in solving constrained convex minimization problem and linear system of ... See full document

... quasi-monotone variational inequalities in infinite-dimensional Hilbert ...the iterative sequence generated by the algorithm for solving the semistrictly quasi-monotone ... See full document

... for solving (.) consists of the linearized projected relaxation methods [, ...multigrid methods were proposed ...complementarity problems and then preconditioners, widely used in the linear ... See full document

... general iterative scheme for finding a common element of the set of solutions of variational inequality problem for an inverse-strongly monotone mapping and the set of fixed points of a ... See full document

... maximal monotone mapping is not very convenient to ...maximal monotone mapping: A monotone mapping B is maximal if and only if for (x, u) ∈ H × H, x – y, u – v ≥  for each (y, v) ∈ G(B) implies u ∈ ... See full document

... that variational inequality, as a greatly important tool, has already been stud- ied for a wide class of unilateral, obstacle, and equilibrium problems arising in several branches of pure and ... See full document

... viscosity iterative algorithm for the implicit midpoint rule of nonexpansive mappings in uniformly smooth ...As applications, we apply our main results to solving fixed point problems of strict ... See full document

... the variational inequality (3). It is well known that the variational inequality theory has emerged as an important tool in studying a wide class of obstacle, unilateral, and ... See full document

... with applications to solving the variational inequality in Banach ...the variational inequality problem in uniformly convex and uniformly smooth Banach spaces and convergence ... See full document

... of variational inequalities, projection methods and its variant form has played an important ...suggest iterative methods for solving mixed variational ...mixed ... See full document

... Variational inequality problems over fixed point sets of nonexpansive mappings include many practical problems in engineering and applied mathematics, and a number of iterative ... See full document

... Variational inequalities were initially investigated by Kinderlehrer and Stampacchia in [], and have been widely studied by many authors ever since, due to the fact that they cover as diverse disciplines as ... See full document

... general iterative method for variational inequality problems, mixed equilibrium problems, and fixed point problems of strictly pseudocontractive mappings in Hilbert spaces,” ... See full document

... new class of generalized extended nonlinear quasi-variational inequality problems involving set-valued relaxed monotone operators and establish its equivalence with the fixed point ... See full document

... new iterative schemes for finding element in F(S)  VI(C, B), see [1]-[3], [5], [8], [13], and reference ...following iterative scheme as the ...strongly monotone mapping of C into H and S be a ... See full document

... Theorem . Let K ⊂ E ∗∗ be a bounded weak* closed convex subset. Suppose that φ : E ∗∗ → R ∪ {+∞} is a lower semi-continuous convex function in the weak* topology K ⊆ D(φ), A : K × K → E ∗ is semi-monotone, and ... See full document

... Next we show the uniqueness of a solution of the variational inequality (.). Suppose that x ∈ F(S) and x ˆ ∈ F(S) are solutions to (.), then, without loss of generality, we may assume that there is a ... See full document

... Iterative methods play an important role in solving variational inequalities. For example, if T is a single-valued, strongly monotone i.e., Tx − Ty, x − y ≥ τx − y 2 for all x, y ∈ K ... See full document

... One can see that the variational inequality problem (1.2) is equivalent to a fixed point prob- lem. That is, an element u ∈ C is a solution of the variational inequality (1.2) if and only if u ... See full document