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\(D\)-invexity and optimality conditions. (English) Zbl 0755.90074

Summary: A generalization of convexity, called \(d\)-invexity, is introduced. Substituting \(d\)-invex for convex, we get some optimality conditions for nondifferentiable multiobjective programming. The application is demonstrated by an example.

MSC:

90C29 Multi-objective and goal programming
49J52 Nonsmooth analysis
26B25 Convexity of real functions of several variables, generalizations
90C30 Nonlinear programming
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References:

[1] Bazaraa, M. S.; Shetty, C. M., Nonlinear programming theory and algorithm (1979), John Wiley and Sons, Inc. · Zbl 0476.90035
[2] Hanson, M. A., On sufficiency of the Kuhn-Tucker condition, J. Math. Anal. Appl., 80, 545-550 (1981) · Zbl 0463.90080
[3] Martin, D. H., The essence of invexity, JOTA, 47, 65-76 (1985) · Zbl 0552.90077
[4] Kaul, R. N.; Kaur, S., Optimality criteria in nonlinear programming involving non-convex functions, J. Math. Anal. Appl., 105, 104-112 (1985) · Zbl 0553.90086
[5] Tanino, T.; Sawaragi, Y., Duality theory in multiobjective programming, JOTA, 27, 509-529 (1979) · Zbl 0378.90100
[6] Y. L. Ye and Q. M. DongJOTA; Y. L. Ye and Q. M. DongJOTA
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