In this article, using a hybrid extragradient method, we introduce a new iterative process for approximating a common element of the set of solutions of an equilibrium problem and a common zero of a finite family of m...
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In this article, using a hybrid extragradient method, we introduce a new iterative process for approximating a common element of the set of solutions of an equilibrium problem and a common zero of a finite family of monotone operators in Hadamard spaces. We also give a numerical example to solve a nonconvex optimization problem in an Hadamard space to support our main result.
We present an extragradient-type algorithm for solving bilevel pseudomonone variational inequalities. The proposed algorithm uses simple projection sequences. Under mild conditions, the convergence of the iteration se...
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We present an extragradient-type algorithm for solving bilevel pseudomonone variational inequalities. The proposed algorithm uses simple projection sequences. Under mild conditions, the convergence of the iteration sequences generated by the algorithm is obtained.
In this paper, we investigate a new extragradient algorithm for solving pseudomonotone equilibrium problems on Hadamard manifolds. Our algorithm uses a variable stepsize, which is updated at each iteration and based o...
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In this paper, we investigate a new extragradient algorithm for solving pseudomonotone equilibrium problems on Hadamard manifolds. Our algorithm uses a variable stepsize, which is updated at each iteration and based on some previous iterates. The convergence analysis of the proposed algorithm is discussed under mild assumptions. In the case where the equilibrium bifunction is strongly pseudomonotone, the R-linear rate of convergence of the new algorithm is formulated. A fundamental experiment is provided to illustrate the numerical behavior of the algorithm.
The variational inequality problem plays an important role in nonlinear analysis and optimization. It is a generalization of the nonlinear complementarity problem. For a variational inequality problem in a Hilbert spa...
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The variational inequality problem plays an important role in nonlinear analysis and optimization. It is a generalization of the nonlinear complementarity problem. For a variational inequality problem in a Hilbert space, the extragradient algorithm with inertial effects has been studied. For a variational inequality problem in a Banach space, Nakajo introduced Haugazeau's hybrid method and Liu introduced the Halpern subgradient extragradient method. In this paper, we construct a new inertial iterative method for solving variational inequality problems in Banach spaces based on the work we mentioned above. We propose a strong convergence theorem. As applications, our result can be used to solve constrained convex minimization problems.
He (J. Inequal. Appl. 2012:Article ID 162 2012) introduced the proximal point CQ algorithm (PPCQ) for solving the split equilibrium problem (SEP). However, the PPCQ converges weakly to a solution of the SEP and is res...
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He (J. Inequal. Appl. 2012:Article ID 162 2012) introduced the proximal point CQ algorithm (PPCQ) for solving the split equilibrium problem (SEP). However, the PPCQ converges weakly to a solution of the SEP and is restricted to monotone bifunctions. In addition, the step-size used in the PPCQ is a fixed constant mu in the interval (0, 1/parallel to A parallel to(2)). This often leads to excessive numerical computation in each iteration, which may affect the applicability of the PPCQ. In order to overcome these intrinsic drawbacks, we propose a robust step-size {mu(n)}(n=1)(infinity) which does not require computation of parallel to A parallel to and apply the adaptive step-size rule on {mu(n)}(n=1)(infinity) in such a way that it adjusts itself in accordance with the movement of associated components of the algorithm in each iteration. Then, we introduce a self-adaptive extragradient-CQ algorithm (SECQ) for solving the SEP and prove that our proposed SECQ converges strongly to a solution of the SEP with more general pseudomonotone equilibrium bifunctions. Finally, we present a preliminary numerical test to demonstrate that our SECQ outperforms the PPCQ.
In this article, we introduce an algorithms by incorporating inertial terms in the extragradient algorithm. A weak convergence theorem is established for the proposed algorithm. Numerical experiments show that the ine...
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In this article, we introduce an algorithms by incorporating inertial terms in the extragradient algorithm. A weak convergence theorem is established for the proposed algorithm. Numerical experiments show that the inertial algorithms speed up the original ones.
In this paper, we investigate the Tseng's extragradient algorithm for non-Lipschitzian variational inequalities with pseudomonotone vector fields on Hadamard manifolds. The convergence analysis of the proposed alg...
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In this paper, we investigate the Tseng's extragradient algorithm for non-Lipschitzian variational inequalities with pseudomonotone vector fields on Hadamard manifolds. The convergence analysis of the proposed algorithm is discussed under mild assumptions. Two experiments are provided to illustrate the asymptotical behavior of the algorithm. The results presented in this paper generalize some known results presented in the literature.
This paper presents an extragradient method for variational inequality associated with a point-to-set vector field in Hadamard manifolds, and a study of its convergence properties. To present our method, the concept o...
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This paper presents an extragradient method for variational inequality associated with a point-to-set vector field in Hadamard manifolds, and a study of its convergence properties. To present our method, the concept of epsilon-enlargement of maximal monotone vector fields is used, and its lower-semicontinuity is established to obtain the method convergence in this new context.
Bearing in mind the notion of monotone vector field on Riemannian manifolds, see [12-16], we study the set of their singularities and for a particularclass of manifolds develop an extragradient-type algorithm converge...
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Bearing in mind the notion of monotone vector field on Riemannian manifolds, see [12-16], we study the set of their singularities and for a particularclass of manifolds develop an extragradient-type algorithm convergent to singularities of such vector fields. In particular, our method can be used forsolving nonlinear constrained optimization problems in Euclidean space, with a convex objective function and the constraint set a constant curvature Hadamard manifold. Our paper shows how tools of convex analysis on Riemannian manifolds can be used to solve some nonconvex constrained problem in a Euclidean space.
In this paper, we introduce a new explicit extragradient algorithm for solving Variational inequality Problem (VIP) in Banach spaces. The proposed algorithm uses a linesearch method whose inner iterations are independ...
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In this paper, we introduce a new explicit extragradient algorithm for solving Variational inequality Problem (VIP) in Banach spaces. The proposed algorithm uses a linesearch method whose inner iterations are independent of any projection onto feasible sets. Under standard and mild assumption of pseudomonotonicity and uniform continuity of the VIP associated operator, we establish the strong convergence of the scheme. Further, we apply our algorithm to find an equilibrium point with minimal environmental cost for a model in electricity production. Finally, a numerical result is presented to illustrate the given model. Our result extends, improves and unifies other related results in the literature.
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