Generalization of preinvex and B-vex functions. (English) Zbl 0802.49026

Summary: A class of functions called \(B\)-preinvex functions is introduced by relaxing the definitions of preinvex and \(B\)-vex functions. Examples are given to show that there exist functions which are \(B\)-preinvex but not preinvex or \(B\)-vex or quasipreinvex. Some of the properties of \(B\)-invex functions are obtained.


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


[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] Ben-Israel, A., andMond, B.,What is Invexity?, Journal of the Australian Mathematical Society, Series B, Vol. 28, pp. 1-9, 1986. · Zbl 0603.90119
[3] Hanson, M. A., andMond, B.,Convex Transformable Programming Problems and Invexity, Journal of Information and Optimization Sciences, Vol. 8, pp. 201-207, 1987. · Zbl 0641.90070
[4] Jeyakumar, W.,Strong and Weak Invexity in Mathematical Programming, Methods of Operations Research, Vol. 55, pp. 109-125, 1985. · Zbl 0566.90086
[5] Weir, T., andMond, B.,Preinvex Functions in Multiple Objective Optimization, Journal of Mathematical Analysis and Applications, Vol. 136, pp. 29-38, 1988. · Zbl 0663.90087
[6] Castagnoli, E., andMazzoleni, P.,About Derivatives of Some Generalized Concave Functions, Continuous Time, Fractional and Multiobjective Programming, Edited by C. Singh and B. K. Dass, Analytic Publishing Company, Delhi, India, pp. 53-65, 1989. · Zbl 0681.90067
[7] Bector, C. R.,Programming Problems with Convex Fractional Functions, Operations Research, Vol. 16, pp. 383-390, 1968. · Zbl 0159.48505
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.