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Numerical Algebra, Control and Optimization (NACO)
 

Some useful inequalities via trace function method in Euclidean Jordan algebras

Pages: 39 - 48, Volume 4, Issue 1, March 2014      doi:10.3934/naco.2014.4.39

 
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Yu-Lin Chang - Department of Mathematics, National Taiwan Normal University, Taipei 11677, Taiwan (email)
Chin-Yu Yang - Department of Mathematics, National Taiwan Normal University, Taipei 11677, Taiwan (email)

Abstract: In this paper, we establish convexity of some functions associated with symmetric cones, called SC trace functions. As illustrated in the paper, these functions play a key role in the development of penalty and barrier function methods for symmetric cone programs. With trace function method we offer much simpler proofs to these useful inequalities.

Keywords:  Symmetric cone, Löwner operator, convexity, trace function.
Mathematics Subject Classification:  Primary: 26A27, 26B05, 26B35, 49J52, 90C33.

Received: May 2013;      Revised: November 2013;      Available Online: December 2013.

 References