A class of nonconvex functions and pre-variational inequalities

Xiaoqi Yang; Guang Ya Chen

doi:10.1016/0022-247X(92)90084-Q

A class of nonconvex functions and pre-variational inequalities

Xiaoqi Yang, Guang Ya Chen

Research output: Journal article publication › Journal article › Academic research › peer-review

103 Citations (Scopus)

Abstract

A class of nonconvex functions is introduced, called semi-preinvex function, which includes the classes of preinvex functions and arc-connected convex functions. The Fritz-John conditions of the mathematical programming problem are derived for these kinds of functions. The pre-variational inequality is given as a necessary condition and also a sufficient condition for a mathematical programming for invex functions. The Type I function related to unconstrained problems is given as an equivalent form of the pre-variational inequality. Existence theorems for the solution of the pre-variational inequality are also proved.

Original language	English
Pages (from-to)	359-373
Number of pages	15
Journal	Journal of Mathematical Analysis and Applications
Volume	169
Issue number	2
DOIs	https://doi.org/10.1016/0022-247X(92)90084-Q
Publication status	Published - 15 Sept 1992
Externally published	Yes

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/0022-247X(92)90084-Q

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AB - A class of nonconvex functions is introduced, called semi-preinvex function, which includes the classes of preinvex functions and arc-connected convex functions. The Fritz-John conditions of the mathematical programming problem are derived for these kinds of functions. The pre-variational inequality is given as a necessary condition and also a sufficient condition for a mathematical programming for invex functions. The Type I function related to unconstrained problems is given as an equivalent form of the pre-variational inequality. Existence theorems for the solution of the pre-variational inequality are also proved.

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DO - 10.1016/0022-247X(92)90084-Q

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A class of nonconvex functions and pre-variational inequalities

Abstract

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