- Research Article
- Open Access
New classes of generalized invex monotonicity
Journal of Inequalities and Applications volume 2006, Article number: 57071 (2006)
This paper introduces new classes of generalized invex monotone mappings and invex cocoercive mappings. Their differential property and role to analyze and solve variational-like inequality problem are presented.
Baiocchi C, Capelo A: Variational and Quasivariational Inequalities. Applications to Free Boundary Problems. John Wiley & Sons, New York; 1984:ix+452.
Crouzeix J-P, Marcotte P, Zhu DL: Conditions ensuring the applicability of cutting-plane methods for solving variational inequalities. Mathematical Programming. Series A 2000,88(3):521–539. 10.1007/PL00011384
Fang YP, Huang NJ: Variational-like inequalities with generalized monotone mappings in Banach spaces. Journal of Optimization Theory and Applications 2003,118(2):327–338. 10.1023/A:1025499305742
Harker PT, Pang J-S: Finite-dimensional variational inequality and nonlinear complementarity problems: a survey of theory, algorithms and applications. Mathematical Programming. Series B 1990,48(2):161–220.
Karamardian S, Schaible S: Seven kinds of monotone maps. Journal of Optimization Theory and Applications 1990,66(1):37–46. 10.1007/BF00940531
Luo HZ, Xu ZK: On characterizations of prequasi-invex functions. Journal of Optimization Theory and Applications 2004,120(2):429–439.
Mohan SR, Neogy SK: On invex sets and preinvex functions. Journal of Mathematical Analysis and Applications 1995,189(3):901–908. 10.1006/jmaa.1995.1057
Osuna-Gómez R, Rufián-Lizana A, Ruíz-Canales P: Invex functions and generalized convexity in multiobjective programming. Journal of Optimization Theory and Applications 1998,98(3):651–661. 10.1023/A:1022628130448
Parida J, Sahoo M, Kumar A: A variational-like inequality problem. Bulletin of the Australian Mathematical Society 1989,39(2):225–231. 10.1017/S0004972700002690
Ruiz-Garzón G, Osuna-Gómez R, Rufián-Lizana A: Generalized invex monotonicity. European Journal of Operational Research 2003,144(3):501–512. 10.1016/S0377-2217(01)00393-9
Yang XQ: On the gap functions of prevariational inequalities. Journal of Optimization Theory and Applications 2003,116(2):437–452. 10.1023/A:1022422407705
Yang XM, Yang XQ, Teo KL: Characterizations and applications of prequasi-invex functions. Journal of Optimization Theory and Applications 2001,110(3):645–668. 10.1023/A:1017544513305
Yang XM, Yang XQ, Teo KL: Generalized invexity and generalized invariant monotonicity. Journal of Optimization Theory and Applications 2003,117(3):607–625. 10.1023/A:1023953823177
Zhu DL, Marcotte P: New classes of generalized monotonicity. Journal of Optimization Theory and Applications 1995,87(2):457–471. 10.1007/BF02192574
Zhu DL, Marcotte P: Co-coercivity and its role in the convergence of iterative schemes for solving variational inequalities. SIAM Journal on Optimization 1996,6(3):714–726. 10.1137/S1052623494250415
About this article
Cite this article
Xu, B., Zhu, D.L. New classes of generalized invex monotonicity. J Inequal Appl 2006, 57071 (2006). https://doi.org/10.1155/JIA/2006/57071
- Monotone Mapping
- Inequality Problem
- Differential Property
- Generalize Invex
- Generalize Invex Monotone