In this paper, we introduce and consider a new system of generalized mixed quasi-variational inclusions with (A, eta)-monotone mappings. We prove the convergence of a new iterative algorithm for this system of general...
详细信息
In this paper, we introduce and consider a new system of generalized mixed quasi-variational inclusions with (A, eta)-monotone mappings. We prove the convergence of a new iterative algorithm for this system of generalized mixed quasi-variational inclusions. Our results can be viewed as a refinement and improvement of the previously known results in the literature. (C) 2009 Elsevier Inc. All rights reserved.
In this paper, we introduce and study a new system of generalized set-valued mixed variational-like inequality problems (SGSMVLIP) and its related auxiliary problems in reflexive Banach spaces. The auxiliary principle...
详细信息
In this paper, we introduce and study a new system of generalized set-valued mixed variational-like inequality problems (SGSMVLIP) and its related auxiliary problems in reflexive Banach spaces. The auxiliary principle technique is applied to study the existence and an iterative algorithm of solutions for the system of generalized set-valued mixed variational-like inequality problems. At first, the existence and uniqueness of solutions of the auxiliary problems for (SGSMVLIP) is shown. Next, an iterative algorithm for solving (SGSMVLIP) is constructed by using the existence and uniqueness result. Finally, we prove the existence of solutions of (SGSMVLIP) and discuss the convergence analysis of the algorithm. These results improve, unify and generalize many corresponding known results given in the literature. (C) 2009 Elsevier B.V. All rights reserved.
Some necessary and sufficient conditions for the existence of a positive definite solution of the nonlinear matrix equation X + A*X(-alpha)A = Q (0 < alpha <= 1) are given. By the way an iterative method is pres...
详细信息
Some necessary and sufficient conditions for the existence of a positive definite solution of the nonlinear matrix equation X + A*X(-alpha)A = Q (0 < alpha <= 1) are given. By the way an iterative method is presented. Furthermore, the convergence and error estimation of the iterative algorithm are derived. The illustrative numerical examples due to Peng are worked out.
Consider a discrete-time nonlinear system with random disturbances appearing in the real plant and the output channel where the randomly perturbed output is measurable. An iterative procedure based on the linear quadr...
详细信息
Consider a discrete-time nonlinear system with random disturbances appearing in the real plant and the output channel where the randomly perturbed output is measurable. An iterative procedure based on the linear quadratic Gaussian optimal control model is developed for solving the optimal control of this stochastic system. The optimal state estimate provided by Kalman filtering theory and the optimal control law obtained from the linear quadratic regulator problem are then integrated into the dynamic integrated system optimisation and parameter estimation algorithm. The iterative solutions of the optimal control problem for the model obtained converge to the solution of the original optimal control problem of the discrete-time nonlinear system, despite model-reality differences, when the convergence is achieved. An illustrative example is solved using the method proposed. The results obtained show the effectiveness of the algorithm proposed.
In this paper, we introduce and study a new class of variational inclusions in Banach spaces. For solving such class of variational inclusions, we introduce a new notion of B-monotone operator and prove the Lipschitz ...
详细信息
In this paper, we introduce and study a new class of variational inclusions in Banach spaces. For solving such class of variational inclusions, we introduce a new notion of B-monotone operator and prove the Lipschitz continuity of the proximal mapping associated with the B-monotone operator. By using the proximal mapping, an iterative algorithm for solving such class of variational inclusions is constructed in Banach spaces. Under some suitable conditions, we prove the convergence of iterative sequence generated by the algorithm. (C) 2009 Elsevier B.V. All rights reserved.
Let H be a Hilbert space. Consider on H a sequence of nonexpansive mappings {T(n)} with common fixed points, an equilibrium function G, a contraction f with coefficient 0< alpha < 1 and a strongly positive linea...
详细信息
Let H be a Hilbert space. Consider on H a sequence of nonexpansive mappings {T(n)} with common fixed points, an equilibrium function G, a contraction f with coefficient 0< alpha < 1 and a strongly positive linear bounded operator A with coefficient (gamma) over bar 0. Let 0 < gamma < (gamma) over bar/alpha We define a suitable Mann type algorithm which strongly converges to the unique solution of the minimization problem(x is an element of C) 1/2 (Ax,x) - h (x), where h is a potential function for f and C is the intersection of the equilibrium points and the common fixed points of the sequence {T(n)}. (C) 2010 Elsevier Ltd. All rights reserved.
We investigate solution properties of a class of evolutionary partial differential equations (PDEs) with viscous and inviscid regularization. An equation in this class of PDEs can be written as an evolution equation, ...
详细信息
We investigate solution properties of a class of evolutionary partial differential equations (PDEs) with viscous and inviscid regularization. An equation in this class of PDEs can be written as an evolution equation, involving only first-order spatial derivatives, coupled with the Helmholtz equation. A recently developed two-step iterative method (P.H. Chiu, L. Lee, T.W.H. Sheu, A dispersion-relation-preserving algorithm for a nonlinear shallow-water wave equation,). Comput. Phys. 228 (2009) 8034-8052) is employed to study this class of PDEs. The method is in principle superior for PDE's in this class as it preserves their physical dispersive features. In particular, we focus on a Leray-type regularization (H.S. Bhat, R.C. Fetecau, A Hamiltonian regularization of the Burgers equation, J. Nonlinear Sci. 16 (2006) 615-638) of the Hopf equation proposed in alternative to the classical Burgers viscous term. We show that the regularization effects induced by the alternative model can be vastly different from those induced by Burgers viscosity depending on the smoothness of initial data in the limit of zero regularization. We validate our numerical scheme by comparison with a particle method which admits closed form solutions. Further effects of the interplay between the dispersive terms comprising the Leray-regularization are illustrated by solutions of equations in this class resulting from regularized Burgers equation by selective elimination of dispersive terms. (C) 2010 Elsevier Inc. All rights reserved.
We study the convergence of two iterative algorithms for finding common fixed points of finitely many Bregman strongly nonexpansive operators in reflexive Banach spaces. Both algorithms take into account possible comp...
详细信息
We study the convergence of two iterative algorithms for finding common fixed points of finitely many Bregman strongly nonexpansive operators in reflexive Banach spaces. Both algorithms take into account possible computational errors. We establish two strong convergence theorems and then apply them to the solution of convex feasibility, variational inequality and equilibrium problems. (C) 2010 Elsevier Ltd. All rights reserved.
The general coupled matrix equations {A(11)X(1)B(11) + A(12)X(2)B(12) + ... + A(1l)X(1l)B(1l) = C-1, A(21)X(1)B(21) + A(22)X(22)B(22) + ... + A(2l)X(l)B(2l) - C-2, (I) . . . A(l1)X(1)B(l1) + A(l2)X(2)B(l2) + ... + A(ll)X(l)B(ll) = C-l, (including the generalized coupled Sylvester matrix equations as special cases) have nice applications in various branches of control and system theory. In this paper, by extending the idea of conjugate gradient method, we propose an efficient iterative algorithm to solve the general coupled matrix equations (I). When the matrix equations (I) are consistent, for any initial matrix group, a solution group can be obtained within finite iteration steps in the absence of roundoff errors. The least Frobenius norm solution group of the general coupled matrix equations can be derived when a suitable initial matrix group is chosen. We can use the proposed algorithm to find the optimal approximation solution group to a given matrix group. ((X) over cap (1);(X) over cap (2), ..., (X) over cap (l) in a Frobenius norm within the solution group set of the matrix equations (I). Also several numerical examples are given to illustrate that the algorithm is effective. Furthermore, the application of the proposed algorithm for solving the system of matrix equations {D1XE1 = F-1, . . . DpXEp = F-p, over (R, S)-symmetric and (R, S)-skew symmetric matrices is highlighted. (C) 2010 Elsevier Ltd. All rights reserved.
In this paper, a new notion of a generalized H-η-accretive operator is introduced and studied, which provides a unifying framework for the generalized m-accretive operator and the H-η-monotone operator in Banach spa...
详细信息
In this paper, a new notion of a generalized H-η-accretive operator is introduced and studied, which provides a unifying framework for the generalized m-accretive operator and the H-η-monotone operator in Banach spaces. A resolvent operator associated with the generalized H-η-accretive operator is defined, and its Lipschitz continuity is shown. As an application, the solvability for a class of variational inclusions involving the generalized H-η-accretive operators in Banach spaces is considered. By using the technique of the resolvent mapping, an iterative algorithm for solving the variational inclusion in Banach spaces is constructed. Under some suitable conditions, it is proven that the solution for the variational inclusion and the convergence of the iterative sequence generated by the algorithm exist.
暂无评论