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ABSTRACT: In this paper, we introduce and analyze a new hybrid extragradient-like iterative algorithm for finding a common solution
of a generalized mixed equilibrium problem, a system of generalized equilibrium problems and a fixed point problem of infinitely
many non expansive mappings. Under some mild conditions, we prove the strong convergence of the sequence generated by the
proposed algorithm to a common solution of these three problems. Such solution also solves an optimization problem. Several
special cases are also discussed. The results presented in this paper are the supplement, extension, improvement and generalization
of the previously known results in this area.
KeywordsGeneralized mixed equilibrium problem–System of generalized equilibrium problems–Optimization problems–Hybrid extragradient-like iterative scheme–Fixed points–Nonexpansive mappings–Strong convergence
Journal of Global Optimization 05/2012; 53(1):69-96. · 1.20 Impact Factor
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ABSTRACT: Pseudomonotone*{_{\ast}} maps are a generalization of paramonotone maps which is very closely related to the cutting plane property in variational
inequality problems (VIP). In this paper, we first generalize the so-called minimum principle sufficiency and the maximum
principle sufficiency for VIP with multivalued maps. Then we show that pseudomonotonicity*{_{\ast}} of the map implies the “maximum principle sufficiency” and, in fact, is equivalent to it in a sense. We then present two
applications of pseudomonotone*{_{\ast}} maps. First we show that pseudomonotone*{_{\ast}} maps can be used instead of the much more restricted class of pseudomonotone+ maps in a cutting plane method. Finally, an application to a proximal point method is given.
Journal of Global Optimization 03/2009; 43(4):565-575. · 1.20 Impact Factor
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J. Global Optimization. 01/2009; 43:565-575.
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J. Global Optimization. 01/2009; 45:297-307.
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ABSTRACT: We first present nine kinds of (generalized) monotone maps and in case of gradient maps their counterpart of nine kinds of
(generalized) convex functions. In addition we present topologically pseudomonotone maps. We then derive sufficient and/or
necessary conditions for various kinds of generalized monotonicity for several subclasses of maps. We study differentiable
maps, locally Lipschitz maps, general continuous maps and affine maps.
12/2004: pages 387-420;
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ABSTRACT: In this paper, we introduce the system of generalized vector equilibrium problems which includes as special cases the system of generalized implicit vector variational inequality problems, the system of generalized vector variational and variational-like inequality problems and the system of vector equilibrium problems. By using a maximal element theorem, we establish existence results for a solution of these systems. As an application, we derive existence results for a solution of a more general Nash equilibrium problem for vector-valued functions.
Journal of Global Optimization 12/2001; 22(1):3-16. · 1.20 Impact Factor
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ABSTRACT: The notion of η-pseudolinearity is introduced. First, some characterizations of an η-pseudolinear function are obtained. Then
characterizations of the solution set of an η-pseudolinear program are derived. The paper generalizes various results on pseudolinear
functions and programs.
Il lavoro introduce la nozione di η-pseudolinearità. Dopo avere ottenuto alcune caratterizzazioni delle funzioni η-pseudolineari,
si derivano caratterizzazioni dell'insieme delle soluzioni di un programma η-pseudolineare. Lo studio generalizza diversi
risultati sulle funzioni e sui programmi pseudolineari.
Rivista di Matematica per le Scienze Economiche e Sociali 04/1999; 22(1):31-39.
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ABSTRACT: Strictly pseudomonotoneZ-maps operating on Banach lattices are considered. Equivalence of complementarity problems and least-element problems is established under certain regularity and growth conditions. This extends a recent result by Riddell (1981) for strictly monotoneZ-maps to the pseudomonotone case. Some other problems equivalent to the above are discussed as well.
Mathematical Programming 09/1995; 70(1):191-200. · 1.71 Impact Factor
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ABSTRACT: In this paper, we report recent developments in solution methods for finding a common element of the fixed point set of a mapping and the solution set of the variational inequality in a Hilbert space. Key–Words: Variational inequality; Asymptotically strict pseudocontractive mapping in the intermediate sense; Fixed point; α-inverse strongly monotone mapping.
