Graphical Derivatives and Stability Analysis for Parameterized Equilibria with Conic Constraints

0449259 - ÚTIA 2016 RIV NL eng J - Journal Article
Mordukhovich, B. S. - Outrata, Jiří - Ramírez, H. C.
Graphical Derivatives and Stability Analysis for Parameterized Equilibria with Conic Constraints.
Set-Valued and Variational Analysis. Roč. 23, č. 4 (2015), s. 687-704. ISSN 1877-0533. E-ISSN 1877-0541
R&D Projects: GA ČR(CZ) GAP201/12/0671
Institutional support: RVO:67985556
Keywords : Variational analysis and optimization * Parameterized equilibria * Conic constraints * Sensitivity and stability analysis * Solution maps * Graphical derivatives * Normal and tangent cones
Subject RIV: BA - General Mathematics
Impact factor: 0.973, year: 2015
http://library.utia.cas.cz/separaty/2015/MTR/outrata-0449259.pdf

The paper concerns parameterized equilibria governed by generalized equations whose multivalued parts are modeled via regular normals to nonconvex conic constraints. Our main goal is to derive a precise pointwise second-order formula for calculating the graphical derivative of the solution maps to such generalized equations that involves Lagrange multipliers of the corresponding KKT systems and critical cone directions. Then we apply the obtained formula to characterizing a Lipschitzian stability notion for the solution maps that is known as isolated calmness.
Permanent Link: http://hdl.handle.net/11104/0251932