Sufficiency of linear transformations on Euclidean Jordan algebras

Author： Qin Linxia  

Publisher： Springer Publishing Company

ISSN： 1862-4472

Source： Optimization Letters, Vol.3, Iss.2, 2009-03, pp. : 265-276

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Abstract

We extend the row-sufficiency and column-sufficiency of a linear transformation from $${mathbb {R}^n}$$ to the setting of Euclidean Jordan algebras. For linear complementarity problems over symmetric cones, we show that the column-sufficiency along with Cross Commutative property is equivalent to the convexity of the solution set, while the row-sufficiency is necessary for the existence of solutions under some conditions.

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