## Related Articles

- Minimization of equilibrium problems, variational inequality problems and fixed point problems. Yao, Yonghong; Liou, Yeong-Cheng; Kang, Shin // Journal of Global Optimization;Dec2010, Vol. 48 Issue 4, p643
In this paper, we devote to find the solution of the following quadratic minimization problem where O is the intersection set of the solution set of some equilibrium problem, the fixed points set of a nonexpansive mapping and the solution set of some variational inequality. In order to solve the...

- Algorithmic Approach to a Minimization Problem. Yonghong Yao; Shin Min Kang; Yeong-Cheng Liou; Zhitao Wu // Abstract & Applied Analysis;2012, p1
We first construct an implicit algorithm for solving the minimization problem minxâˆˆÎ©â€–xâ€–, where Î© is the intersection set of the solution set of some equilibrium problem, the fixed points set of a nonexpansive mapping, and the solution set of some variational inequality....

- STRONG CONVERGENCE OF A GENERAL IMPLICIT ALGORITHM FOR VARIATIONAL INEQUALITY PROBLEMS AND EQUILIBRIUM PROBLEMS AND A CONTINUOUS REPRESENTATION OF NONEXPANSIVE MAPPINGS. BAMI, M. LASHKARIZADEH; SOORI, E. // Bulletin of the Iranian Mathematical Society;2014, Vol. 40 Issue 4, p977
We introduce a general implicit algorithm for finding a common element of the set of solutions of systems of equilibrium problems and the set of common fixed points of a sequence of nonexpansive mappings and a continuous representation of nonexpansive mappings. Then we prove the strong...

- Hybrid Gradient-Projection Algorithm for Solving Constrained Convex Minimization Problems with Generalized Mixed Equilibrium Problems. Ceng, Lu-Chuan; Wen, Ching-Feng // Journal of Function Spaces & Applications;2012, p1
It is well known that the gradient-projection algorithm (GPA) for solving constrained convex minimization problems has been proven to have only weak convergence unless the underlying Hilbert space is finite dimensional. In this paper, we introduce a new hybrid gradient-projection algorithm for...

- ITERATIVE ALGORITHMS FOR FAMILIES OF VARIATIONAL INEQUALITIES FIXED POINTS AND EQUILIBRIUM PROBLEMS. Saeidi, S. // Bulletin of the Iranian Mathematical Society;Apr2011, Vol. 37 Issue 1, p247
We introduce an iterative algorithm for finding a common element of the set of fixed points for an infinite family of nonexpansive mappings, the set of solutions of the variational inequalities for a family of Î±-inverse-strongly monotone mappings and the set of solutions of a system of...

- An Extragradient Method for Mixed Equilibrium Problems and Fixed Point Problems. Yonghong Yao; Yeong-Cheng Liou; Yuh-Jenn Wu // Fixed Point Theory & Applications;2009, Special section p1
The purpose of this paper is to investigate the problem of approximating a common element of the set of fixed points of a demicontractive mapping and the set of solutions of a mixed equilibrium problem. First, we propose an extragradient method for solving the mixed equilibrium problems and the...

- Hybrid Iterative Algorithm of Asymptotically Non-expansive Mappings for Equilibrium Problems. Shanshan Yang; Jingxin Zhang // International Journal of Hybrid Information Technology;2014, Vol. 7 Issue 3, p303
Optimization problems, variational inequalities, minimax problems can be formulated as equilibrium problems. The iterative algorithms of fixed points are often applied to finding the solution of equilibrium problems. In this paper, we introduce a new hybrid iterative algorithm for finding a...

- Steepest-Descent Approach to Triple Hierarchical Constrained Optimization Problems. Lu-Chuan Ceng; Cheng-Wen Liao; Chin-Tzong Pang; Ching-Feng Wen // Abstract & Applied Analysis;2014, p1
We introduce and analyze a hybrid steepest-descent algorithm by combining Korpelevich's extragradient method, the steepest-descent method, and the averaged mapping approach to the gradient-projection algorithm. It is proven that under appropriate assumptions, the proposed algorithm converges...

- A New Algorithm for Constrained Matrix Least Squares Approximations. Wei-Yong Yan; Moore, John B. // Annals of Operations Research;2000, Vol. 98 Issue 1-4, p255
This paper considers the problem of approximating a given symmetric matrix by a symmetric matrix with a prescribed spectrum so that the Frobenius norm of the matrix difference is minimized. By the introduction of a variable search direction, a new convergent algorithm for solving the problem is...

- Hybrid Projection Algorithms for Generalized Equilibrium Problems and Strictly Pseudocontractive Mappings. Jong Kyu Kim; Sun Young Cho; Xiaolong Qin // Journal of Inequalities & Applications;2010, Vol. 2010, p1
The purpose of this paper is to consider the problem of finding a common element in the solution set of equilibrium problems and in the fixed point set of a strictly pseudocontractive mapping. Strong convergence of the purposed hybrid projection algorithm is obtained in Hilbert spaces.