# On localizing global Pareto solutions in a given convex set

Agnieszka Drwalewska; Lesław Gajek

Applicationes Mathematicae (1999)

- Volume: 26, Issue: 4, page 383-394
- ISSN: 1233-7234

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topDrwalewska, Agnieszka, and Gajek, Lesław. "On localizing global Pareto solutions in a given convex set." Applicationes Mathematicae 26.4 (1999): 383-394. <http://eudml.org/doc/219247>.

@article{Drwalewska1999,

abstract = {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.},

author = {Drwalewska, Agnieszka, Gajek, Lesław},

journal = {Applicationes Mathematicae},

keywords = {sufficient and necessary conditions for optimality; Pareto optimal solutions; dual cones; feasible directions},

language = {eng},

number = {4},

pages = {383-394},

title = {On localizing global Pareto solutions in a given convex set},

url = {http://eudml.org/doc/219247},

volume = {26},

year = {1999},

}

TY - JOUR

AU - Drwalewska, Agnieszka

AU - Gajek, Lesław

TI - On localizing global Pareto solutions in a given convex set

JO - Applicationes Mathematicae

PY - 1999

VL - 26

IS - 4

SP - 383

EP - 394

AB - 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.

LA - eng

KW - sufficient and necessary conditions for optimality; Pareto optimal solutions; dual cones; feasible directions

UR - http://eudml.org/doc/219247

ER -

## References

top- [1] B. D. Craven, Mathematical Programming and Control Theory, Halsted, London, 1982.
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- [3] L. Gajek and D. Zagrodny, Existence of maximal points with respect to ordered bipreference relations, J. Optim. Theory Appl. 70 (1991), 355-364. Zbl0748.90061
- [4] L. Gajek and D. Zagrodny, Countably orderable sets and their applications in optimization, Optimization 26 (1992), 287-301. Zbl0815.49020
- [5] L. Gajek and D. Zagrodny, Weierstrass theorem for monotonically semicontinuous functions, ibid. 29 (1994), 199-203. Zbl0817.49010
- [6] B. Pshenichnyĭ, Necessary Conditions for an Extremum, Nauka, Moscow, 1982 (in Russian).
- [7] S. Rolewicz, On drop property, Studia Math. 85 (1987), 27-35. Zbl0642.46011
- [8] W. Rudin, Functional Analysis, Moscow, Mir, 1975 (in Russian); English original: McGraw-Hill, New York, 1973.
- [9] C. Swartz, Pshenichnyĭ's theorem for vector minimization, J. Optim. Theory Appl. 53 (1987), 309-317. Zbl0595.90080

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