Some P-properties for linear transformations on Euclidean Jordan algebras

Gowda, M. Seetharama; Sznajder, Roman; Tao, Jiyuan

doi:10.1016/j.laa.2004.03.028

Cited by 207 publications

(138 citation statements)

References 24 publications

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“…"(a) ⇒ (b)" Since (a) holds, the elements x, y operator commute by Proposition 6 in [5]. Thus, there is a Jordan frame {e 1 , · · · , e r } such that x = r i=1 x i e i and y = r i=1 y i e i .…”

Section: Theorem 2 If G(·) Is Locally Lipschitz Onmentioning

confidence: 91%

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Monotonicity of Löwner operators and its applications to symmetric cone complementarity problems

2010

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We prove necessary and sufficient conditions for locally Lipschitz Löwner operators to be monotone, strictly monotone and strongly monotone. Utilizing our characterization of the strict monotonicity of Löwner operators, we generalize Mangasarian class of Nonlinear Complementarity Problem (NCP)-functions to the setting of symmetric cone complementarity problem. This affirmatively answers a question of Tseng [Math. Program. 83, 159-185(1998)].

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Section: Theorem 2 If G(·) Is Locally Lipschitz Onmentioning

confidence: 91%

“…SCCP provides a simple, natural, and unified framework for various existing complementarity problems, such as the NCP, SDCP and the second-order cone complementarity problem (SOCCP); see, e.g., [3,5,6,8,11,14,21].…”

mentioning

confidence: 99%

Monotonicity of Löwner operators and its applications to symmetric cone complementarity problems

2010

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“…We recall the following from Gowda, Sznajder and Tao [10]: Proposition 2.3: For x, y ∈ V , the following conditions are equivalent:…”

Section: Proofmentioning

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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“…Every l i (x)(i {1,..., r}) is called an eigenvalue of x, which is a continuous function with respect to x (see [20]). Define Tr(x) := r i=1 λ i (x), where Tr(x) denotes the trace of x.…”

Section: Euclidean Jordan Algebramentioning

confidence: 99%

A smoothing-type algorithm for solving inequalities under the order induced by a symmetric cone

Zhang

2011

J Inequal Appl

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In this article, we consider the numerical method for solving the system of inequalities under the order induced by a symmetric cone with the function involved being monotone. Based on a perturbed smoothing function, the underlying system of inequalities is reformulated as a system of smooth equations, and a smoothing-type method is proposed to solve it iteratively so that a solution of the system of inequalities is found. By means of the theory of Euclidean Jordan algebras, the algorithm is proved to be well defined, and to be globally convergent under weak assumptions and locally quadratically convergent under suitable assumptions. Preliminary numerical results indicate that the algorithm is effective.

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Some P-properties for linear transformations on Euclidean Jordan algebras

Cited by 207 publications

References 24 publications

Monotonicity of Löwner operators and its applications to symmetric cone complementarity problems

Monotonicity of Löwner operators and its applications to symmetric cone complementarity problems

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

A smoothing-type algorithm for solving inequalities under the order induced by a symmetric cone

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