Lipschitz continuity of the gradient of a one-parametric class of SOC merit functions

DOI10.1080/02331930802180319zbMath1196.26018OpenAlexW1991805540MaRDI QIDQ2786315

Jein-Shan Chen, Shaohua Pan

Publication date: 21 September 2010

Published in: Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/02331930802180319

zbMATH Keywords

spectral factorizationLipschitz continuitymerit functionsecond-order cone

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 (1)

Expected residual minimization formulation for a class of stochastic linear second-order cone complementarity problems

Cites Work

• Analysis of nonsmooth vector-valued functions associated with second-order cones.
• Monotone functions on formally real Jordan algebras
• Two classes of merit functions for the second-order cone complementarity problem
• The \(SC^1\) property of the squared norm of the SOC Fischer-Burmeister function
• A new class of semismooth Newton-type methods for nonlinear complementarity problems
• Strong semismoothness of the Fischer-Burmeister SDC and SOC complementarity functions
• A note on the Lipschitz continuity of the gradient of the squared norm of the matrix-valued Fischer-Burmeister function
• An unconstrained smooth minimization reformulation of the second-order cone complementarity problem
• Smoothing Functions for Second-Order-Cone Complementarity Problems
• A special newton-type optimization method
• A Combined Smoothing and Regularization Method for Monotone Second-Order Cone Complementarity Problems

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