Abstract
We show that penalized functions of the Fischer–Burmeister and the natural residual functions defined on symmetric cones are complementarity functions. Boundedness of the solution set of a symmetric cone complementarity problem, based on the penalized natural residual function, is proved under monotonicity and strict feasibility. The proof relies on a trace inequality on Euclidean Jordan algebras.
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This work was supported by KOSEF Grant No. R01-2006-000-10211-0.
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Kum, S., Lim, Y. Penalized complementarity functions on symmetric cones. J Glob Optim 46, 475–485 (2010). https://doi.org/10.1007/s10898-009-9450-y
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DOI: https://doi.org/10.1007/s10898-009-9450-y