Smoothing Functions for Second-Order-Cone Complementarity Problems

By Masao Fukushima, Zhi-Quan Tom Luo, Paul Tseng. SIAM Journal on Optimization, 2002

408 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/d528470348ff1bff542accaabadecd9f5e58e196

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Citations in the corpus

On the Coderivative of the Projection Operator onto the Second-order Cone (2008, background): “Similarly to [6] and [3], we benefit in our analysis from strong results, valid in Jordan algebras on symmetric cones, cf.”
Interior Gradient and Proximal Methods for Convex and Conic Optimization (2006, positive): “…using (4.25) it follows that the unique solution u ≡ z ∈ L n ++ of (4.22) is given by z It is worthwhile to mention that an alternative derivation of (4.27) could also have been obtained by using properties and facts on Jordan algebra associated with the second order cone; see, e.g., [22, 23].”
A survey on SOC complementarity functions and solution methods for SOCPs and SOCCPs (2012, methodology): “3) of [25] is equivalent to requiring the positive semidefiniteness of F ′.”
The convex and monotone functions associated with second-order cone (2006, methodology): “For any function f : R ! R, the following vector-valued function associated with K (n 1) was considered [8,10]:”
Smoothing methods for nonsmooth, nonconvex minimization (2012, neutral): “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].”
A Damped Gauss-Newton Method for the Second-Order Cone Complementarity Problem (2009, methodology): “The function was shown in [11] to satisfy the equivalence (6), and therefore its squared norm”
Some P-properties for linear transformations on Euclidean Jordan algebras (2004, neutral): “The next two results are well known when V is: R with cone R +, S with semidefinite cone S+, or L with the Lorentz cone L+, see [3,9,30].”