SOC-monotone and SOC-convex functions vs. matrix-monotone and matrix-convex functions

DOI10.1016/j.laa.2012.04.030zbMath1247.26019OpenAlexW1978549503MaRDI QIDQ442689

Yungyen Chiang, Shaohua Pan, Jein-Shan Chen

Publication date: 3 August 2012

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2012.04.030

zbMATH Keywords

Hilbert spacesecond-order coneSOC-convexitySOC-monotonicity

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) (90C33) Continuity and differentiation questions (26B05) Special properties of functions of several variables, Hölder conditions, etc. (26B35)

Related Items

Monotonicity and circular cone monotonicity associated with circular cones ⋮ Parabolic second-order directional differentiability in the Hadamard sense of the vector-valued functions associated with circular cones ⋮ The P-class and Q-class functions on symmetric cones

Uses Software

• PENSDP

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A merit function method for infinite-dimensional SOCCPs
• Double piling structure of matrix monotone functions and of matrix convex functions
• Differential analysis of matrix convex functions
• On the solution of large-scale SDP problems by the modified barrier method using iterative solvers
• Some characterizations for SOC-monotone and SOC-convex functions
• Some results on matrix monotone functions
• Jensen's inequality for operators and Loewner's theorem
• Perturbation analysis of second-order cone programming problems
• Smoothing Functions for Second-Order-Cone Complementarity Problems
• The convex and monotone functions associated with second-order cone
• Concavity of monotone matrix functions of finite order
• Monotone operator functions, gaps and power moment problem
• A Class of Interior Proximal-Like Algorithms for Convex Second-Order Cone Programming
• GAPS BETWEEN CLASSES OF MATRIX MONOTONE FUNCTIONS
• On some operator monotone functions