Computation of the epsilon-subdifferential of convex piecewise linear-quadratic functions in optimal worst-case time

DOI10.1007/s11228-018-0476-5OpenAlexW3099414708MaRDI QIDQ2328199

Deepak Kumar, Yves Lucet

Publication date: 9 October 2019

Published in: Set-Valued and Variational Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1803.01074

zbMATH Keywords

visualizationconvex functionsubdifferentialcomputer-aided convex analysispiecewise linear-quadratic functions\(\epsilon\)-subdifferentialscomputational convex analysis (CCA)

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10)

Related Items (1)

New global optimality conditions for nonsmooth DC optimization problems

Uses Software

• na24
• na13
• fenchel
• SCAT
• CCA

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Convexity of the proximal average
• The optimal value and optimal solutions of the proximal average of convex functions
• The piecewise linear-quadratic model for computational convex analysis
• Fast Moreau envelope computation I: Numerical algorithms
• Symbolic Fenchel conjugation
• Faster than the fast Legendre transform, the linear-time Legendre transform
• A fast computational algorithm for the Legendre-Fenchel transform
• Visualization of the \(\varepsilon \)-subdifferential of piecewise linear-quadratic functions
• A linear-time approximate convex envelope algorithm using the double Legendre-Fenchel transform with application to phase separation
• Self-Dual Smooth Approximations of Convex Functions via the Proximal Average
• Graph-Matrix Calculus for Computational Convex Analysis
• Symbolic computation of multidimensional Fenchel conjugates
• Approximate Subdifferentials and Applications. I: The Finite Dimensional Theory
• A Proximal Average for Nonconvex Functions: A Proximal Stability Perspective
• What Shape Is Your Conjugate? A Survey of Computational Convex Analysis and Its Applications
• The Proximal Average: Basic Theory
• Variational Analysis
• On Computing the Nested Sums and Infimal Convolutions of Convex Piecewise-Linear Functions
• Symbolic computation of Fenchel conjugates
• On the Subdifferentiability of Convex Functions
• Techniques and Open Questions in Computational Convex Analysis
• Convex analysis and monotone operator theory in Hilbert spaces

This page was built for publication: Computation of the epsilon-subdifferential of convex piecewise linear-quadratic functions in optimal worst-case time