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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
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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 · doi:10.1007/BF00939919
[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 · doi:10.1016/0022-247X(81)90123-2
[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 · doi:10.1016/0022-247X(85)90099-X
[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 · doi:10.1016/0022-247X(88)90135-7
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