Linearly perturbed generalized polyhedral normal cone mappings and applications. (2nd January 2016)

• Record Type: Journal Article
• Authors: Ban, Liqun; Song, Wen
• Is Part Of: Optimization. Volume 65:Number 1(2016)
• Page Start: 9
• Page End: 34
• Publication Date: 2016-01-02
• Subjects: reflexive Banach spaces -- perturbed generalized polyhedral sets -- parametric variational inequalities -- robust Lipschitz stability -- coderivatives; 90C31 sensitivity -- stability -- parametric optimization; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2014.979819
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : Under a mild regularity assumption, we derive an exact formula for the Fréchet coderivative and some estimates for the Mordukhovich coderivative of the normal cone mappings of perturbed generalized polyhedra in reflexive Banach spaces. Assume in addition that the generating elements are linearly independent and some qualification condition holds, the Lipschitzian stability of the parameterized variational inequalities over the right-hand side perturbed generalized polyhedra is characterized using the initial data.