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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.

90C29Multi-objective programming; goal programming
49J52Nonsmooth analysis (other weak concepts of optimality)
26B25Convexity and generalizations (several real variables)
90C30Nonlinear programming
Full Text: DOI
[1] Bazaraa, M. S.; Shetty, C. M.: Nonlinear programming theory and algorithm. (1979) · 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. Dong, Optimality conditions in constrained nondifferentiable programming, JOTA, to be published.