Two pairs of families of polyhedral norms versus \(\ell _p\)-norms: proximity and applications in optimization

DOI10.1007/s10107-015-0899-9zbMath1352.47047OpenAlexW2103971090MaRDI QIDQ263209

Stan Uryasev, Jun-Ya Gotoh

Publication date: 4 April 2016

Published in: Mathematical Programming. Series A. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10107-015-0899-9

zbMATH Keywords

\(\ell_p\)-norm\(p\)th order cone programming (\(p\)OCP)CVaR normdeltoidal normlinear programming (LP)

Mathematics Subject Classification ID

Applications of mathematical programming (90C90) Special polytopes (linear programming, centrally symmetric, etc.) (52B12) Quadratic programming (90C20) Linear programming (90C05) Norms (inequalities, more than one norm, etc.) of linear operators (47A30) Polyhedra and polytopes; regular figures, division of spaces (51M20) Applications of operator theory in optimization, convex analysis, mathematical programming, economics (47N10) Inequalities and extremum problems in real or complex geometry (51M16) Symmetry properties of polytopes (52B15)

Related Items (7)

A fair division approach to humanitarian logistics inspired by conditional value-at-risk ⋮ Polytopal balls arising in optimization ⋮ Support vector machines based on convex risk functions and general norms ⋮ DC formulations and algorithms for sparse optimization problems ⋮ Unnamed Item ⋮ Norm induced polyhedral uncertainty sets for robust linear optimization ⋮ Two pairs of families of polyhedral norms versus \(\ell _p\)-norms: proximity and applications in optimization

Uses Software

• CVX
• Portfolio Safeguard

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Two pairs of families of polyhedral norms versus \(\ell _p\)-norms: proximity and applications in optimization
• CVaR (superquantile) norm: stochastic case
• On max-stable processes and the functional \(D\)-norm
• CVaR norm and applications in optimization
• Support vector machines based on convex risk functions and general norms
• A note on the complexity of \(L _{p }\) minimization
• Robust linear optimization under general norms.
• Equality relating Euclidean distance cone to positive semidefinite cone
• Polyhedral approximations inp-order cone programming
• Graph Implementations for Nonsmooth Convex Programs
• The Price of Robustness
• An Efficient Algorithm for Minimizing a Sum of p-Norms
• Regularization and Variable Selection Via the Elastic Net
• Higher moment coherent risk measures
• On Polyhedral Approximations of the Second-Order Cone

This page was built for publication: Two pairs of families of polyhedral norms versus \(\ell _p\)-norms: proximity and applications in optimization