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Linear Inequalities Over Complex Cones

Published online by Cambridge University Press:  20 November 2018

Abraham Berman
Abraham Berman*
Affiliation:
Université De Montréal, Montréal Québec
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The basic solvability theorems of Farkas [2] and Levinson [4] were recently extended in different directions by Ben-Israel [1] and Kaul [3].

The theorem stated in this note generalizes both results of Ben-Israel and Kaul and is applicable to nonlinear programming over complex cones.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 16 , Issue 1 , March 1973 , pp. 19 - 21
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Ben-Israel, A., Linear equations and inequalities on finite dimensional, real or complex, vector spaces:. A unified theory, J. Math. Anal. Appl. 27 (1969), 367–389.Google Scholar
2. Farkas, J., Uber die Th?orie des einfachen Ungleichungen, J. Reine Angew. Math. 124 (1902), 1–24.Google Scholar
3. Kaul, R. N., On linear inequalities in complex space, Amer. Math. Monthl. 77 (1970), 955-960.Google Scholar
4. Levinson, N., Linear programming in complex space, J. Math. Anal. Appl. 14 (1966), 44–62.Google Scholar