×

\(D\)-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
PDFBibTeX XMLCite
Full Text: DOI

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
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.