The piecewise linear-quadratic model for computational convex analysis

DOI10.1007/s10589-007-9124-yzbMath1186.90089OpenAlexW2133898219MaRDI QIDQ842774

Heinz H. Bauschke, Yves Lucet, Mike Trienis

Publication date: 25 September 2009

Published in: Computational Optimization and Applications (Search for Journal in Brave)

Full work available at URL: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.318.5177

zbMATH Keywords

convex analysisLegendre-Fenchel transformMoreau envelopeMoreau-Yosida approximateFenchel conjugatecomputational convex analysisproximal average

Mathematics Subject Classification ID

Analysis of algorithms and problem complexity (68Q25) Convex programming (90C25) Algorithms for approximation of functions (65D15)

Related Items (13)

Self-Dual Smooth Approximations of Convex Functions via the Proximal Average ⋮ Graph-Matrix Calculus for Computational Convex Analysis ⋮ Computing the conjugate of convex piecewise linear-quadratic bivariate functions ⋮ Convexity conditions and the Legendre-fenchel transform for the product of finitely many positive definite quadratic forms ⋮ The resolvent average on symmetric cones ⋮ Convex hull algorithms for piecewise linear-quadratic functions in computational convex analysis ⋮ Convexity of the proximal average ⋮ Convex parametric piecewise quadratic optimization: theory and algorithms ⋮ Computing the partial conjugate of convex piecewise linear-quadratic bivariate functions ⋮ Visualization of the \(\varepsilon \)-subdifferential of piecewise linear-quadratic functions ⋮ Duality and Convex Programming ⋮ Computation of the epsilon-subdifferential of convex piecewise linear-quadratic functions in optimal worst-case time ⋮ Linear-Time Convexity Test for Low-Order Piecewise Polynomials

Uses Software

• Scilab
• na24
• na13
• fenchel
• SCAT

Cites Work

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• Symbolic computation of Fenchel conjugates
• How to Transform One Convex Function Continuously into Another
• Proximité et dualité dans un espace hilbertien
• Convex Analysis

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