×

The notion of \(V\)-\(r\)-invexity in differentiable multiobjective programming. (English) Zbl 1140.90485

Summary: A generalization of convexity, namely \(V\)-\(r\)-invexity, is considered in the case of nonlinear multiobjective programming problems where the functions involved are differentiable. The assumptions on Pareto solutions are relaxed by means of \(V\)-\(r\)-invex functions. Also some duality results are obtained for such optimization problems.

MSC:

90C29 Multi-objective and goal programming
26B25 Convexity of real functions of several variables, generalizations
90C26 Nonconvex programming, global optimization
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Antczak T., Zeszyty Nauk. Politech. Rzeszowskiej Mat. 25 pp 5– (2001)
[2] Antczak T., J. Math. Anal. Appl. 263 pp 355– (2001) · Zbl 1051.90018
[3] Antczak T., J. Math. Anal. Appl. 264 pp 382– (2001) · Zbl 1052.90072
[4] Avriel M., Math. Program. 2 pp 309– (1972) · Zbl 0249.90063
[5] Ben-Israel A., J. Austral. Math. Soc. Ser. B 28 pp 1– (1986) · Zbl 0603.90119
[6] Craven B. D., Bull. Austral. Math. Soc. 24 pp 357– (1981) · Zbl 0452.90066
[7] Craven B. D., J. Austral. Math. Soc. Ser. A 39 pp 1– (1985)
[8] Egudo R. R., J. Math. Anal. Appl. 126 pp 469– (1987) · Zbl 0635.90086
[9] Hanson M. A., J. Math. Anal. Appl. 80 pp 545– (1981) · Zbl 0463.90080
[10] Jeyakumar V., J. Austral. Math. Soc. Ser. B 34 pp 43– (1992) · Zbl 0773.90061
[11] Kanniappan P., J. Optim. Theory Appl. 40 pp 167– (1983) · Zbl 0488.49007
[12] Luc D. T., Bull. Austral. Math. Soc. 46 pp 47– (1992) · Zbl 0755.90072
[13] Martin D. H., J. Optim. Theory Appl. 47 pp 65– (1985) · Zbl 0552.90077
[14] Osuna-Gomez R., J. Math. Anal. Appl. 233 pp 205– (1999) · Zbl 0928.90083
[15] Pareto V., Switzerland pp 1897– (1896)
[16] Singh C., J. Optim. Theory Appl. 53 pp 115– (1987) · Zbl 0593.90071
[17] Srivastava M. K., Opsearch 31 pp 266– (1995)
[18] Weir T., Opsearch 25 pp 98– (1988)
[19] Wolfe P., Quart. Appl. Math. 19 pp 239– (1961)
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.