On localizing global Pareto solutions in a given convex set
Drwalewska, Agnieszka ; Gajek, Lesław
Applicationes Mathematicae, Tome 26 (1999), p. 383-394 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

Sufficient conditions are given for the global Pareto solution of the multicriterial optimization problem to be in a given convex subset of the domain. In the case of maximizing real valued-functions, the conditions are sufficient and necessary without any convexity type assumptions imposed on the function. In the case of linearly scalarized vector-valued functions the conditions are sufficient and necessary provided that both the function is concave and the scalarization is increasing with respect to the cone generating the preference relation.

Publié le : 1999-01-01
EUDML-ID : urn:eudml:doc:219247 
@article{bwmeta1.element.bwnjournal-article-zmv26i4p383bwm,
     author = {Agnieszka Drwalewska and Les\l aw Gajek},
     title = {On localizing global Pareto solutions in a given convex set},
     journal = {Applicationes Mathematicae},
     volume = {26},
     year = {1999},
     pages = {383-394},
     zbl = {1010.90071},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-zmv26i4p383bwm}
}

Drwalewska, Agnieszka; Gajek, Lesław. On localizing global Pareto solutions in a given convex set. Applicationes Mathematicae, Tome 26 (1999) pp. 383-394. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-zmv26i4p383bwm/

[000] [1] B. D. Craven, Mathematical Programming and Control Theory, Halsted, London, 1982.

[001] [2] R. Engelking, General Topology, Monograf. Mat. 60, PWN, Warszawa, 1977.

[002] [3] L. Gajek and D. Zagrodny, Existence of maximal points with respect to ordered bipreference relations, J. Optim. Theory Appl. 70 (1991), 355-364. | Zbl 0748.90061

[003] [4] L. Gajek and D. Zagrodny, Countably orderable sets and their applications in optimization, Optimization 26 (1992), 287-301. | Zbl 0815.49020

[004] [5] L. Gajek and D. Zagrodny, Weierstrass theorem for monotonically semicontinuous functions, ibid. 29 (1994), 199-203. | Zbl 0817.49010

[005] [6] B. Pshenichnyĭ, Necessary Conditions for an Extremum, Nauka, Moscow, 1982 (in Russian).

[006] [7] S. Rolewicz, On drop property, Studia Math. 85 (1987), 27-35. | Zbl 0642.46011

[007] [8] W. Rudin, Functional Analysis, Moscow, Mir, 1975 (in Russian); English original: McGraw-Hill, New York, 1973.

[008] [9] C. Swartz, Pshenichnyĭ's theorem for vector minimization, J. Optim. Theory Appl. 53 (1987), 309-317. | Zbl 0595.90080