Abstract
This paper defines a new class of generalized type I functions, and obtains Kuhn-Tucker necessary and sufficient conditions and duality results for constrained optimization problems in the presence of the aforesaid weaker assumptions on the objective and constraint functions involved in the problem.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
M. A Hanson, On sufficiency of the Kuhn-Tucker conditions, J. of Mathematical Analysis and Applications, 1981, 80(2): 545–550.
B. D. Craven and B. M. Glover, Invex functions and duality, J. of the Australian Mathematical Society Series A, 1985, 39(1): 1–20.
M. A. Hanson and B. Mond, Necessary and sufficient conditions in constrained optimization, Mathematical Programming, 1987, 37(1): 51–58.
M. A. Hanson, A single solution of the van der Waerden permanent problem, J. of Global Optimization, 1991, 1: 287–293.
R. Pini and C. Singh, A survey of recent [1985–1995] advances in generalized convexity with applications to duality and optimality conditions, Optimization, 1997, 39: 311–360.
S. K. Mishra and G. Giorgi, Invexity and Optimization, Nonconvex Optimization and Its Applications 88, Springer-Verlag, Berlin-Heidelberg, 2008.
N. G. Rueda and M. A. Hanson, Optimality criteria in mathematical programming involving generalized invexity, J. of Mathematical Analysis and Applications, 1988, 130(2): 375–385.
R. N. Kaul, S. K. Suneja, and M. K. Srivastava, Optimality criteria and duality in multiple-objective optimization involving generalized invexity, J. of Optimization Theory and Applications, 1994, 80(3): 465–482.
G. Caristi, M. Ferrara, and A. Stefanescu, New invexity-type conditions in constrained optimization, Proceedings of the 6th International Symposium on Generalized Convexity / Monotonicity, Lecture Notes in Economics and Mathematical Systems No. 502 (ed. by N. Hadjisavvas, J. E. Martinez Legaz, and J. P. Penot), Springer, 2001: 159–166.
D. H. Martin, The essence of invexity, J. of Optimization Theory and Applications, 1985, 47(1): 65–76.
S. K. Mishra and N. G. Rueda, On univexity-type nonlinear programming problems, Bulletin of the Allahabad Mathematical Society, 2001, 16: 105–113.
Z. K. Xu, On invexity-type nonlinear programming problems, J. of Optimization Theory and Applications, 1994, 80(1): 135–148.
Author information
Authors and Affiliations
Additional information
This paper was recommended for publication by Editor Shouyang WANG.
Rights and permissions
About this article
Cite this article
Mishra, S.K., Rueda, N.G. Generalized invexity-type conditions in constrained optimization. J Syst Sci Complex 24, 394–400 (2011). https://doi.org/10.1007/s11424-011-8234-x
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11424-011-8234-x