The \(SC^1\) property of the squared norm of the SOC Fischer-Burmeister function

DOI10.1016/j.orl.2007.08.005zbMath1152.90621OpenAlexW2102054728MaRDI QIDQ943805

Jie Sun, Defeng Sun, Jein-Shan Chen

Publication date: 10 September 2008

Published in: Operations Research Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.orl.2007.08.005

zbMATH Keywords

spectral factorizationLipschitz continuitymerit functionsemismoothnesssecond-order cone

Mathematics Subject Classification ID

Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) (90C33)

Related Items (12)

Smoothing functions and algorithm for nonsymmetric circular cone complementarity problems. ⋮ Nonsingularity conditions for FB system of reformulating nonlinear second-order cone programming ⋮ On the generalized Fischer-Burmeister merit function for the second-order cone complementarity problem ⋮ A proximal gradient descent method for the extended second-order cone linear complementarity problem ⋮ Lipschitz continuity of the gradient of a one-parametric class of SOC merit functions ⋮ A new class of smoothing complementarity functions over symmetric cones ⋮ Symmetrization of generalized natural residual function for NCP ⋮ A linearly convergent derivative-free descent method for the second-order cone complementarity problem ⋮ A smoothing-type algorithm for the second-order cone complementarity problem with a new nonmonotone line search ⋮ A one-parametric class of merit functions for the symmetric cone complementarity problem ⋮ Convergence properties of a smoothing approach for mathematical programs with second-order cone complementarity constraints ⋮ A perturbation approach for an inverse quadratic programming problem over second-order cones

Cites Work

• Analysis of nonsmooth vector-valued functions associated with second-order cones.
• Monotone functions on formally real Jordan algebras
• Merit functions for semi-definite complementarity problems
• The Minnesota notes on Jordan algebras and their applications. Edited and annotated by Aloys Krieg and Sebastian Walcher
• Complementarity functions and numerical experiments on some smoothing Newton methods for second-order-cone complementarity problems
• A nonsmooth version of Newton's method
• 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
• Iterative Solution of Nonlinear Equations in Several Variables

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