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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.

MSC:

49M37 Numerical methods based on nonlinear programming
49J52 Nonsmooth analysis
49K27 Optimality conditions for problems in abstract spaces
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[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
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