Convexity and differentiability properties of spectral functions and spectral mappings on Euclidean Jordan algebras

Baes, Michel

doi:10.1016/j.laa.2006.11.025

Cited by 75 publications

(65 citation statements)

References 20 publications

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“…For the discussion of next section, we propose the favorable properties of the distance measure H, and the following two technical lemmas will be used, the first lemma is given by M.Baes [19].…”

Section: Properties Of Distance-like Functionmentioning

confidence: 99%

On the Convergence of Central Path and Generalized Proximal Point Method for Symmetric Cone Linear Programming

Yu¹,

Zhu²,

Qian-qian³

2013

Appl. Math. Inf. Sci.

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Section: Properties Of Distance-like Functionmentioning

confidence: 99%

On the Convergence of Central Path and Generalized Proximal Point Method for Symmetric Cone Linear Programming

Yu¹,

Zhu²,

Qian-qian³

2013

Appl. Math. Inf. Sci.

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“…This inequality (and the corresponding equality characterization) has been extended to simple Euclidean Jordan algebras by Lim, Kim, and Faybusovich [15] based on Lie algebraic ideas, and by Baes [1] based on Birkhoff's theorem on doubly stochastic matrices. See also [4] for a proof based on hyperbolic polynomials.…”

Section: Corollary 44mentioning

confidence: 99%

The Cauchy interlacing theorem in simple Euclidean Jordan algebras and some consequences

Gowda

Tao

2011

Linear and Multilinear Algebra

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“…Applying Theorem 6.3 in [14], the function a → tr(a − ) = (ϕ • λ)(a) is convex and therefore tr( x+y 2 ) − ≤ 1 2 tr(x − ) + 1 2 tr(y − ) or tr(x + y) − ≤ tr(x − ) + tr(y − ). Similarly we can obtain the third trace inequality.…”

Section: Lemma 41 Let K Be the Cone Of Squares Of A Euclidean Jordanmentioning

confidence: 99%

A new class of complementarity functions for symmetric cone complementarity problems

Wang

Wei

2010

Optim Lett

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A popular approach to solving the complementarity problem is to reformulate it as an equivalent equation system via a complementarity function. In this paper, we propose a new class of functions, which contains the penalized natural residual function and the penalized Fischer-Burmeister function for symmetric cone complementarity problems. We show that this class of functions is indeed a class of complementarity functions. We finally prove that the merit function of this new class of complementarity functions is coercive.

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Convexity and differentiability properties of spectral functions and spectral mappings on Euclidean Jordan algebras

Cited by 75 publications

References 20 publications

On the Convergence of Central Path and Generalized Proximal Point Method for Symmetric Cone Linear Programming

On the Convergence of Central Path and Generalized Proximal Point Method for Symmetric Cone Linear Programming

The Cauchy interlacing theorem in simple Euclidean Jordan algebras and some consequences

A new class of complementarity functions for symmetric cone complementarity problems

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