Skip to main content

New classes of generalized invex monotonicity

Abstract

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.

[123456789101112131415]

References

  1. 1.

    Baiocchi C, Capelo A: Variational and Quasivariational Inequalities. Applications to Free Boundary Problems. John Wiley & Sons, New York; 1984:ix+452.

    Google Scholar 

  2. 2.

    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

    MATH  MathSciNet  Article  Google Scholar 

  3. 3.

    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

    MATH  MathSciNet  Article  Google Scholar 

  4. 4.

    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.

    MATH  MathSciNet  Article  Google Scholar 

  5. 5.

    Karamardian S, Schaible S: Seven kinds of monotone maps. Journal of Optimization Theory and Applications 1990,66(1):37–46. 10.1007/BF00940531

    MATH  MathSciNet  Article  Google Scholar 

  6. 6.

    Luo HZ, Xu ZK: On characterizations of prequasi-invex functions. Journal of Optimization Theory and Applications 2004,120(2):429–439.

    MATH  MathSciNet  Article  Google Scholar 

  7. 7.

    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

    MATH  MathSciNet  Article  Google Scholar 

  8. 8.

    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

    MATH  MathSciNet  Article  Google Scholar 

  9. 9.

    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

    MATH  MathSciNet  Article  Google Scholar 

  10. 10.

    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

    MATH  MathSciNet  Article  Google Scholar 

  11. 11.

    Yang XQ: On the gap functions of prevariational inequalities. Journal of Optimization Theory and Applications 2003,116(2):437–452. 10.1023/A:1022422407705

    MATH  MathSciNet  Article  Google Scholar 

  12. 12.

    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

    MATH  MathSciNet  Article  Google Scholar 

  13. 13.

    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

    MATH  MathSciNet  Article  Google Scholar 

  14. 14.

    Zhu DL, Marcotte P: New classes of generalized monotonicity. Journal of Optimization Theory and Applications 1995,87(2):457–471. 10.1007/BF02192574

    MATH  MathSciNet  Article  Google Scholar 

  15. 15.

    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

    MATH  MathSciNet  Article  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to B. Xu.

Rights and permissions

Reprints and Permissions

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

Download citation

Keywords

  • Monotone Mapping
  • Inequality Problem
  • Differential Property
  • Generalize Invex
  • Generalize Invex Monotone
\