Stability Analysis for Composite Optimization Problems and Parametric Variational Systems

B. S. Mordukhovich () and M. E. Sarabi ()
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B. S. Mordukhovich: Wayne State University
M. E. Sarabi: Miami University

Journal of Optimization Theory and Applications, 2017, vol. 172, issue 2, No 11, 554-577

Abstract: Abstract This paper aims to provide various applications for second-order variational analysis of extended-real-valued piecewise linear functions recently obtained by the authors. We mainly focus here on establishing relationships between full stability of local minimizers in composite optimization and Robinson’s strong regularity of associated (linearized and nonlinearized) KKT systems. Finally, we address Lipschitzian stability of parametric variational systems with convex piecewise linear potentials.

Keywords: Variational analysis and optimization; Piecewise linear functions; Second-order subdifferentials; Nondegeneracy; Full stability of local minimizers; Strong regularity of KKT systems; Lipschitzian stability of parametric variational systems; 49J52; 90C30; 90C31 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10957-016-1039-2

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