zbMATH — the first resource for mathematics

New classes of generalized monotonicity. (English) Zbl 0837.65067
Summary: This paper introduces new classes of generalized monotone functions and relates them to classes previously introduced.

65K10 Numerical optimization and variational techniques
90C25 Convex programming
49J40 Variational inequalities
Full Text: DOI
[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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.