Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-24T08:46:24.791Z Has data issue: false hasContentIssue false
  • English
  • Français

Semi-Compactness with Respect to a Euclidean Cone

Published online by Cambridge University Press:  20 November 2018

Daniel H. Wagner
Daniel H. Wagner*
Affiliation:
Associates Station Square One, Paoli, Pennsylvania 19301
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Our motivation for this note originates with consideration of a subset A of Euclidean w-space, Rn, which contains only part of its boundary. The part contained is t h a t part of the closure of A which cannot be “bettered“ within A with respect to the preference associated with a fixed closed convex cone Γ. Here b is preferred to a if and only if a — b ∊ Γ; if, for instance, Γ is the non-negative orthant of Rn, this preference is ordinary vector inequality.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 29 , Issue 1 , 01 February 1977 , pp. 29 - 36
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. Olech, C., Integrals of set valued functions and linear optimal control problems, IFAC, Fourth Congress of the International Federation of Automatic Control, Warsaw, June 16-21 (1969), 22–35.Google Scholar
2. Olech, C. Integrals of set-valued functions and linear optimal control problems, Proceedings of the Colloquium on Optimal Control Theory, Brussels (1969), 109–125.Google Scholar
3. Rockafellar, R. T., Convex analysis (Princeton University Press, 1970).CrossRefGoogle Scholar
4. Wagner, D. H., Integral of a set-valued fmiction with semi-closed values, Journal of Mathematical Analysis and Applications, 55 (1976), 616–633.Google Scholar
5. Wagner, D. H. and Stone, L. D., Necessity and existence results on constrained optimization of separable Junctionals by a multiplier rule, SIAM Journal on Control 12 (1974), 356–372.Google Scholar
6. Yu, P. L., Cone convexity, cone extreme points, and nondominated solutions in decision problems with multiobjectives, J. Optimization Theory Appl. 14 (1974), 319–377.Google Scholar