Sequential extremal principle and necessary conditions for minimizing sequences
Year: 2025
Type: article
Abstract: The conventional definition of extremality of a finite collection of sets is extended by replacing a fixed point (extremal point) in the intersection of the sets by a collection of sequences of points in the individual sets with the distances between the corresponding points tending to zero. This allows one to consider collections of unbounded sets with empty intersection. Exploiting the ideas behind the conventional extremal principle, we derive an extended sequential version of the latter result in terms of Fréchet and Clarke normals. Sequential versions of the related concepts of stationarity, approximate stationarity and transversality of collections of sets are also studied. As an application, we establish sequential necessary conditions for minimizing (and more general firmly stationary, stationary and approximately stationary) sequences in a constrained optimization problem.
Source: Optimization
Authors: Nguyen Duy Cuong, Alexander Y. Kruger
Institutions: Can Tho University, Ton Duc Thang University
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4413060601