A Chain Rule for Strict Twice Epi-Differentiability and Its Applications
From MaRDI portal
Publication:6195317
DOI10.1137/22m1520025arXiv2209.01489OpenAlexW4392294126MaRDI QIDQ6195317
M. Ebrahim Sarabi, Nguyen T. V. Hang
Publication date: 13 March 2024
Published in: SIAM Journal on Optimization (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2209.01489
chain rulegeneralized equationsproximal mappingnondegenerate solutionsstrict proto-differentiabilitystrict twice epi-differentiabilityregularity of subdifferential
Sensitivity, stability, parametric optimization (90C31) Nonsmooth analysis (49J52) Set-valued and variational analysis (49J53) Numerical methods for mathematical programming, optimization and variational techniques (65K99)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Differentiability properties of metric projections onto convex sets
- Second-order analysis of piecewise linear functions with applications to optimization and stability
- Maximal monotone relations and the second derivatives of nonsmooth functions
- Primal superlinear convergence of SQP methods in piecewise linear-quadratic composite optimization
- Variational convexity and the local monotonicity of subgradient mappings
- Forward-backward quasi-Newton methods for nonsmooth optimization problems
- Smoothness of the metric projection onto nonconvex bodies in Hilbert spaces
- Augmented Lagrangians and hidden convexity in sufficient conditions for local optimality
- Characterizations of Full Stability in Constrained Optimization
- Generalized Second Derivatives of Convex Functions and Saddle Functions
- Strong Metric (Sub)regularity of Karush–Kuhn–Tucker Mappings for Piecewise Linear-Quadratic Convex-Composite Optimization and the Quadratic Convergence of Newton’s Method
- Geometrical interpretation of the predictor-corrector type algorithms in structured optimization problems
- First- and Second-Order Epi-Differentiability in Nonlinear Programming
- Normal Maps Induced by Linear Transformations
- Variational Analysis
- Tilt Stability of a Local Minimum
- Forward-Backward Envelope for the Sum of Two Nonconvex Functions: Further Properties and Nonmonotone Linesearch Algorithms
- Characterizations of Strong Regularity for Variational Inequalities over Polyhedral Convex Sets
- Generalized Hessian Properties of Regularized Nonsmooth Functions
- Prox-regular functions in variational analysis
- Second-Order Subdifferential Calculus with Applications to Tilt Stability in Optimization
- Parabolic regularity in geometric variational analysis
- Variational Analysis of Regular Mappings
- Generalized Newton Algorithms for Tilt-Stable Minimizers in Nonsmooth Optimization
- Active‐Set Newton Methods and Partial Smoothness
- Variational Analysis of Composite Models with Applications to Continuous Optimization
- Twice Epi-Differentiability of Extended-Real-Valued Functions with Applications in Composite Optimization
- Local Convergence Analysis of Augmented Lagrangian Methods for Piecewise Linear-Quadratic Composite Optimization Problems
- Alternating Projections on Manifolds
- Implicit Functions and Solution Mappings
- On a Class of Nonsmooth Composite Functions
