×

Generalized B-vex functions and generalized B-vex programming. (English) Zbl 0802.49027

Summary: A class of functions called pseudo \(B\)-vex and quasi \(B\)-vex functions is introduced by relaxing the definitions of \(B\)-vex, pseudoconvex, and quasiconvex functions. Similarly, the class of \(B\)-invex, pseudo \(B\)- invex, and quasi \(B\)-invex functions is defined as a generalization of \(B\)-vex, pseudo \(B\)-vex, and quasi \(B\)-vex functions. The sufficient optimality conditions and duality results are obtained for a nonlinear programming problem involving \(B\)-vex and \(B\)-invex functions.

MSC:

49M37 Numerical methods based on nonlinear programming
49J52 Nonsmooth analysis
49K27 Optimality conditions for problems in abstract spaces
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Bector, C. R., andSingh, C.,B-Vex Functions, Journal of Optimization Theory and Applications, Vol. 71, pp. 237-253, 1991. · Zbl 0793.90069
[2] Bector, C. R.,Mathematical Analysis of Some Nonlinear Programming Problems, PhD Thesis, Indian Institute of Technology, Kanpur, India, 1968. · Zbl 0159.48505
[3] Castagnoli, E., andMazzoleni, P.,About Derivatives of Some Generalized Concave Functions, Journal of Information and Optimization Sciences, Vol. 10, pp. 53-65, 1989. · Zbl 0681.90067
[4] Hanson, M. A.,On Sufficiency of Kuhn-Tucker Conditions, Journal of Mathematical Analysis and Applications, Vol. 80, pp. 545-550, 1981. · Zbl 0463.90080
[5] Kaul, R. N., andKaur, S.,Optimality Criteria in Nonlinear Programming Involving Nonconvex Functions, Journal of Mathematical Analysis and Applications, Vol. 105, pp. 104-112, 1985. · Zbl 0553.90086
[6] Mond, B., andWeir, T.,Generalized Concavity and Duality, Generalized Concavity in Optimization and Economics, Edited by S. Schaible and W. T. Ziemba, Academic Press, New York, New York, pp. 263-279, 1981.
[7] Mangasarian, O. L.,Nonlinear Programming, McGraw-Hill, New York, New York, 1969.
[8] Mond, B., andWeir, T.,Preinvex Functions in Multiple Objective Optimization, Journal of Mathematical Analysis and Applications, Vol. 136, pp. 28-38, 1988. · Zbl 0667.49001
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.