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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

Abstract

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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.

How to cite

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Drwalewska, 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

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  1. [1] B. D. Craven, Mathematical Programming and Control Theory, Halsted, London, 1982. 
  2. [2] R. Engelking, General Topology, Monograf. Mat. 60, PWN, Warszawa, 1977. 
  3. [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. [4] L. Gajek and D. Zagrodny, Countably orderable sets and their applications in optimization, Optimization 26 (1992), 287-301. Zbl0815.49020
  5. [5] L. Gajek and D. Zagrodny, Weierstrass theorem for monotonically semicontinuous functions, ibid. 29 (1994), 199-203. Zbl0817.49010
  6. [6] B. Pshenichnyĭ, Necessary Conditions for an Extremum, Nauka, Moscow, 1982 (in Russian). 
  7. [7] S. Rolewicz, On drop property, Studia Math. 85 (1987), 27-35. Zbl0642.46011
  8. [8] W. Rudin, Functional Analysis, Moscow, Mir, 1975 (in Russian); English original: McGraw-Hill, New York, 1973. 
  9. [9] C. Swartz, Pshenichnyĭ's theorem for vector minimization, J. Optim. Theory Appl. 53 (1987), 309-317. Zbl0595.90080

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