A new look at smoothing Newton methods for nonlinear complementarity problems and box constrained variational inequalities

By Liqun Qi, Defeng Sun, Guanglu Zhou. Mathematical programming, 2000

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A survey on SOC complementarity functions and solution methods for SOCPs and SOCCPs (2012, methodology): “Therefore, under the nonsingularity assumption of ∂BΘ(ω ∗), using the similar arguments to those of [54], we can establish the following local superlinear (or quadratic) convergence results.”
Smoothing methods for nonsmooth, nonconvex minimization (2012, background): “See [1,2,4–7,14,16–18,20,22,24–31,33,39,40,46–50,54,56–60,63,64, 66,70,72,73,81,82,88–92,94,97,103,104].”
SMOOTHING METHODS FOR COMPLEMENTARITY PROBLEMS AND THEIR APPLICATIONS : A SURVEY (2000, methodology): “Introduction Smoothing methods have been developed for solving many important optimization problems including complementarity problems [3, 5, 8, 10, 13, 16, 33, 35, 37, 47, 48, 54, 57], variational inequalities [2, 17, 19, 30, 49], optimal control problems [39], semi-in nite programs [55], mathemati”
Numerical comparisons based on four smoothing functions for absolute value equation (2018, methodology): “An alternative approach is to recast the AVE as a system of nonsmooth equations and then tackle with the nonsmooth equations by applying nonsmooth Newton algorithm [18] or smoothing Newton algorithm [19].”