Zhu, D.; Marcotte, P. New classes of generalized monotonicity. (English) Zbl 0837.65067 J. Optimization Theory Appl. 87, No. 2, 457-471 (1995). Summary: This paper introduces new classes of generalized monotone functions and relates them to classes previously introduced. Cited in 25 Documents MSC: 65K10 Numerical optimization and variational techniques 90C25 Convex programming 49J40 Variational inequalities Keywords:variational inequalities; generalized monotonicity; pseudomonotone mappings; pseudoconvexity; convergence; iterative algorithms; cocoercive mappings PDFBibTeX XMLCite \textit{D. Zhu} and \textit{P. Marcotte}, J. Optim. Theory Appl. 87, No. 2, 457--471 (1995; Zbl 0837.65067) Full Text: DOI References: [1] Karamardian, S., andSchaible, S.,Seven Kinds of Monotone Maps, Journal of Optimization Theory and Applications, Vol. 66, pp. 37–46, 1990. · Zbl 0679.90055 · doi:10.1007/BF00940531 [2] Schaible, S.,Generalized Monotonicity, Proceedings of the 10th International Summer School on Nonsmooth Optimization, Analysis, and Applications, Erice, Italy, 1991; Edited by F. Giannessi Gordon and Breach, Amsterdam, The Netherlands, 1992. [3] Zhu, D., andMarcotte, P.,Cocoercivity and Its Role in the Convergence of Iterative Schemes for Solving Variational Inequality Problems, Preprint, Centre de Recherche sur les Transports, Université de Montréal, 1992. [4] Tseng, P.,Further Applications of a Splitting Algorithm to Decomposition in Variational Inequalities and Convex Programming, Mathematical Programming, Vol. 48, pp. 249–264, 1990. · Zbl 0725.90079 · doi:10.1007/BF01582258 [5] Magnanti, T. L., andPerakis, G.,Convergence Conditions for Variational Inequality Algorithms, Working Paper OR-282-93, Massachusetts Institute of Technology, 1993. [6] Luo, Z., andTseng, P.,A Decomposition Property for a Class of Square Matrices, Applied Mathematical Letters, Vol. 4, pp. 67–69, 1991. · Zbl 0733.15006 · doi:10.1016/0893-9659(91)90148-O [7] Ortega, J. M., andRheinboldt, W. C.,Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York, New York, 1970. · Zbl 0241.65046 [8] Marcotte, P., andWu, J. H.,On the Convergence of Projection Methods: Application to the Decomposition of Affine Variational Inequalities, Journal of Optimization Theory and Applications, Vol. 85, pp. 347–362, 1995. · Zbl 0831.90104 · doi:10.1007/BF02192231 [9] Gowda, M. S.,Pseudomonotone and Copositive Star Matrices, Linear Algebra and Its Applications, Vol. 113, pp. 107–118, 1989. · Zbl 0661.15018 · doi:10.1016/0024-3795(89)90289-9 [10] Auslender, A.,Optimisation: Méthodes Numériques, Masson, Paris, France, 1976. [11] Karamardian, S., Schaible, S., andCrouzeix, J. P.,Characterizations of Generalized Monotone Maps, Journal of Optimization Theory and Applications, Vol. 76, pp. 399–413, 1993. · Zbl 0792.90070 · doi:10.1007/BF00939374 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.