Calculus for Directional Limiting Normal Cones and Subdifferentials

• DOI: 10.1007/s11228-018-0492-5
• Publication Date: 2018-08-14T11:37:58Z
• Authors: Matúš Benko; Helmut Gfrerer; Jiří V. Outrata
• Keywords: 49J53, 49J52, 90C31; Qualification conditions; Optimization and Control (math.OC); Directional limiting normal cone; FOS: Mathematics; 0211 other engineering and technologies; Directional limiting subdifferential; 02 engineering and technology; Generalized differential calculus; Mathematics - Optimization and Control

The paper is devoted to the development of a comprehensive calculus for directional limiting normal cones, subdifferentials and coderivatives in finite dimensions. This calculus encompasses the whole range of the standard generalized differential calculus for (non-directional) limiting notions and relies on very weak (non-restrictive) qualification conditions having also a directional character. The derived rules facilitate the application of tools exploiting the directional limiting notions to difficult problems of variational analysis including, for instance, various stability and sensitivity issues. This is illustrated by some selected applications in the last part of the paper.<br/>28 pages<br/>