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A note on convex cones in topological vector spaces

Published online by Cambridge University Press:  17 April 2009

Alicia Sterna-Karwat
Alicia Sterna-Karwat
Affiliation:
Department of Mathematics, Monash University, Clayton, Victoria, 3168, Australia.
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Abstract

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The aim of the present note is an independent study of a class of convex cones, which is the largest possible with regard to existence of cone-maximal points in abstract vector optimization problems.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 35 , Issue 1 , February 1987 , pp. 97 - 109
Copyright
Copyright © Australian Mathematical Society 1987

References

[1]Borwein, J.M., “The geometry of Pareto efficiency over cones”. Math. Operationsforsch. Statist. Ser. Optim. 11 (1980) 235–248.Google Scholar
[2]Borwein, J.M., “On the existence of Pareto efficient points”. Math. Oper. Res. 8 (1983) 64–73.CrossRefGoogle Scholar
[3]Hartley, R., “On cone-efficiency, cone-convexity and cone-compactness”, STAM J. Appl. Math. 34 (1978) 211–222.Google Scholar
[4]Hazen, G.B., Morin, T.L., “Optimality conditions in non-conical multiple objective programming”, J. Optim. Theory Appl. 40 (1983) 25 – 60.CrossRefGoogle Scholar
[5]Holmes, R.B., Geometric Functional Analysis and Its Applications (Springer-Verlag, New York, 1975).CrossRefGoogle Scholar
[6]Lipecki, Z., “On some dense subspaces of topological linear spaces”, Studia Math. 77 (1984) 413 – 421.CrossRefGoogle Scholar
[7]Penot, J.P., Sterna-Karwat, A., “Parameterized multicriteria optimization; continuity and closedness of optimal multifunctions”, J. Math. Anal. Appl. (to appear).Google Scholar
[8]Sterna-Karwat, A., “On existence of cone-maximal points in real topological linear spaces”, Israel J. Math (to appear).Google Scholar
[9]Sterna-Karwat, A., “A note on cone-maximal and extreme points in topological vector spaces”, Analysis Paper 49, Monash University (1985), submitted.Google Scholar