Twice epi-differentiability of extended-real-valued functions with applications in composite optimization

2019/11/13 by Mohammadi, Ashkan, Sarabi, M. Ebrahim · 4 citations
#FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.1911.05236

Abstract

The paper is devoted to the study of the twice epi-differentiablity of extended-real-valued functions, with an emphasis on functions satisfying a certain composite representation. This will be conducted under the parabolic regularity, a second-order regularity condition that was recently utilized in [13] for second-order variational analysis of constraint systems. Besides justifying the twice epi-differentiablity of composite functions, we obtain precise formulas for their second subderivatives under the metric subregularity constraint qualification. The latter allows us to derive second-order optimality conditions for a large class of composite optimization problems.

Cited by

• Complete Characterizations of Well-Posedness in Parametric Composite Optimization
• Proximal gradient methods in Banach spaces
• Second-Order Characterizations of Tilt Stability in Composite Optimization
• Characterizations of Strong Variational Sufficiency in General Models of Composite Optimization

Related

• A Chain Rule for Strict Twice Epi-Differentiability and its Applications
• Twice epi-differentiablity and parabolic regularity of a class of non-amenable functions
• Twice Epi-Differentiability of Orthogonally Invariant Matrix Functions and Application
• Variational Analysis of Composite Models with Applications to Continuous\n Optimization
• Parabolic Regularity of Spectral Functions