Some optimality conditions in vector optimization. (English) Zbl 0676.90073
Summary: By means of a theorem of the alternative for generalized systems, weak alternative is introduced and some necessary and/or sufficient optimality conditions such as a generalized saddle-point condition is deduced; a simple proof of the Fritz John conditions for multiobjective functions is given.
MSC:
| 90C31 | Sensitivity, stability, parametric optimization |
| 49K10 | Optimality conditions for free problems in two or more independent variables |
References:
| [1] | Bitran G.R., J.O.T.A. 29 (4) pp 573– (1979) · Zbl 0389.52021 · doi:10.1007/BF00934453 |
| [2] | Borwein J.M., Math. Programming 13 pp 163– (1977) · Zbl 0375.90062 · doi:10.1007/BF01584336 |
| [3] | Cambini A., Lecture Notes in Math. 1190, in: Optimization and Related Fields (1986) · doi:10.1007/BFb0076702 |
| [4] | Cambini A., Optimization and Operations Research Section, Paper 120, in: Separation functions and optimality conditions in vector extremum problems (1984) |
| [5] | Giannessi F., J.O.T.A. 42 (3) (1984) · Zbl 0504.49012 · doi:10.1007/BF00935321 |
| [6] | Martein L., J.O.T.A. 47 (2) pp 217– (1985) · Zbl 0549.49016 · doi:10.1007/BF00940770 |
| [7] | Martein L., Optimization and Operations Research Section, Paper 133, in: Semistationary points and necessary conditions in vector extremum problems (1986) |
| [8] | Martein L., Optimization and Operations Research Section, Paper 136, in: Some results on regularity of vector extremum problems (1986) |
| [9] | Sarawagi V., J.O.T.A. 27 pp 509– (1979) · Zbl 0378.90100 · doi:10.1007/BF00933437 |
| [10] | White D.J., Mathematical Programming 31 pp 192– (1985) · Zbl 0579.90083 · doi:10.1007/BF02591748 |
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