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Zbl 1051.90018
Antczak, Tadeusz
$(p,r)$-invex sets and functions. (English)
[J] J. Math. Anal. Appl. 263, No. 2, 355-379 (2001). ISSN 0022-247X

Summary: Notions of invexity of a function and of a set are generalized. The notion of an invex function with respect to $\eta$ can be further extended with the aid of $p$-invex sets. Slight generalization of the notion of $p$-invex sets with respect to $\eta$ leads to a new class of functions. A family of real functions called, in general, $(p, r)$-pre-invex functions with respect to $\eta$ (without differentiability) or $(p,r)$-invex functions with respect to $\eta$ (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 $\eta$ .

MSC 2000:: *90C26 Nonconvex programming
26B25 Convexity and generalizations (several real variables)
90C29 Multi-objective programming, etc.

Keywords: $(p,r)$-invex set with respect to $\eta$; $r$-invex set with respect to $\eta$; $(p,r)$-pre-invex function with respect to $\eta$; $(p,r)$-invex function with respect to $\eta$

Cited in: Zbl 1154.26015 Zbl 1109.26009

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