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(p, r)-Invex Sets and Functions

✍ Scribed by Tadeusz Antczak

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 169 KB
Volume: 263
Category: Article
ISSN: 0022-247X
DOI: 10.1006/jmaa.2001.7574

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✦ Synopsis

Notions of invexity of a function and of a set are generalized. The notion of an invex function with respect to η can be further extended with the aid of p-invex sets. Slight generalization of the notion of p-invex sets with respect to η leads to a new class of functions. A family of real functions called, in general, p r -preinvex functions with respect to η (without differentiability) or p r -invex functions with respect to η (in the differentiable case) is introduced. Some (geometric) properties of these classes of functions are derived. Sufficient optimality conditions are obtained for a nonlinear programming problem involving p r -invex functions with respect to η.

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(p,&#xa0;r)-Invex Sets and Functions

✦ Synopsis

(p, r)-Invex Sets and Functions