Subvexormal Functions and Subvex Functions

X. F. Li and J. L. Dong
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X. F. Li: Jilin University of Technology
J. L. Dong: Jilin University of Technology

Journal of Optimization Theory and Applications, 1999, vol. 103, issue 3, No 10, 675-704

Abstract: Abstract Subvexormal functions and subinvexormal functions are proposed, whose properties are shared commonly by most generalized convex functions and most generalized invex functions, respectively. A necessary and sufficient condition for a subvexormal function to be subinvexormal is given in the locally Lipschitz and regular case. Furthermore, subvex functions and subinvex functions are introduced. It is proved that the class of strictly subvex functions is equivalent to that of functions whose local minima are global and that, in the locally Lipschitz and regular case, both strongly subvex functions and strongly subinvex functions can be characterized as functions whose relatively stationary points (slight extension of stationary points) are global minima.

Keywords: Subvexormal functions; subinvexormal functions; subvexity; subinvexity; locally Lipschitz functions; relatively stationary points; local minima; global minima (search for similar items in EconPapers)
Date: 1999
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DOI: 10.1023/A:1021744309992

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