×

zbMATH — the first resource for mathematics

On some sufficient optimality conditions in multiobjective differentiable programming. (English) Zbl 0784.90070
Summary: Some results on sufficient optimality conditions in multiobjective differentiable programming are established under generalized \(F\)- convexity assumptions. Various levels of convexity on the component of the functions involved are imposed, and the equality constraints are not necessarily linear. In the nonlinear case scalarization of the objective function is used.

MSC:
90C29 Multi-objective and goal programming
90C30 Nonlinear programming
PDF BibTeX XML Cite
Full Text: EuDML Link
References:
[1] A. Ben-Israel, B. Mond: What is invexity?. J. Austral. Math. Soc. 28 (1986), 1-9. · Zbl 0603.90119
[2] M. A. Hanson: On sufficiency on the Kuhn-Tucker conditions. J. Math. Annal. Appl. 80 (1981), 545 - 550. · Zbl 0463.90080
[3] M.A. Hanson, B. Mond: Further generalizations of convexity in mathematical programming. J. Inform. Optim. Sci. 3 (1982), 25-32. · Zbl 0475.90069
[4] I. Jahn: Scalarization in vector optimization. Math. Programming 29 (1984), 203-218. · Zbl 0539.90093
[5] J.G. Lin: Maximal vector and multiobjective optimization. J. Optim. Theory Appl. 18 (1976), 41-64. · Zbl 0298.90056
[6] D.T. Luc: Scalarization of vector optimization problems. J. Optim. Theory Appl. 55 (1987), 85- 102. · Zbl 0622.90083
[7] I. Marusciac: On Fritz John type optimality criterion in multiobjective optimization. Anal. Numer. Theor. Approx. 11 (1982), 109-114. · Zbl 0501.90081
[8] B. Mond: Generalized convexity in mathematical programming. Bull. Austral. Math. Soc. 27 (1983), 185-202. · Zbl 0502.90066
[9] A. Pascoletti, P. Serafini: Scalarizing vector optimization problems. J. Optim. Theory Appl. 42 (1984), 499-524. · Zbl 0505.90072
[10] C. Singh: Duality theory in multiobjective differentiable programming. J. Inform. Optim. Sci. 9 (1988), 231-240. · Zbl 0651.90079
[11] C. Singh: Optimality conditions in multiobjective differentiable programming. J. Optim. Theory Appl. 53 (1987), 115-123. · Zbl 0593.90071
[12] C. Singh, M.A. Hanson: Saddlepoint theory for nondifferentiable multiobjective fractional programming. J. Optim. Theory Appl. 51 (1986), 41-48. · Zbl 0593.90077
[13] W. Standler: A survey of multicriteria optimization or the vector maximum problem. Part I: 1776-1960. J. Optim. Theory Appl. 29 (1979), 1-52. · Zbl 0388.90001
[14] A. Takayama: Mathematical Economics. The Dryden Press, Hinsdale, Illinois 1974. · Zbl 0313.90008
[15] A.W. Tucker: Dual systems of homogeneous linear relations. Linear Inequalities and Related Systems (H.W. Kuhn, A.W. Tucker. Princeton University Press, Princeton, New Jersey 1956. · Zbl 0072.37503
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.