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Invexity criteria for a class of vector-valued functions

Published online by Cambridge University Press:  17 April 2009

Pham Huu Sach  and
Ta Duy Phuong
Pham Huu Sach
Affiliation:
Hanoi Institute of MathematicsPO Box 631Boho, HanoiVietnam
Ta Duy Phuong
Affiliation:
Hanoi Institute of MathematicsPO Box 631Boho, HanoiVietnam
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Abstract

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This paper gives criteria, necessary or sufficient for a vector-valued function F = (f1, f2, …, fk) to be invex. Here each fi is of the -class (that is, each fi is a function whose gradient mapping is locally Lipschitz in a neighbourhood of x0) and the invexity of F means that F(x) − F(x0) ⊂ ˚F′(X) + Q for a fixed convex cone Q of Rk and every x near x0 (˚F′ being the Jacobian matrix of F at x0).

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 51 , Issue 2 , April 1995 , pp. 249 - 262
Copyright
Copyright © Australian Mathematical Society 1995

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