On the coerciveness of some merit functions for complementarity problems over symmetric cones |
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Authors: | Deren Han |
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Affiliation: | School of Mathematics and Computer Sciences, Nanjing Normal University, Nanjing 210097, PR China |
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Abstract: | One of the popular solution methods for the complementarity problem over symmetric cones is to reformulate it as the global minimization of a certain merit function. An important question to be answered for this class of methods is under what conditions the level sets of the merit function are bounded (the coerciveness of the merit function). In this paper, we introduce the generalized weak-coerciveness of a continuous transformation. Under this condition, we prove the coerciveness of some merit functions, such as the natural residual function, the normal map, and the Fukushima-Yamashita function for complementarity problems over symmetric cones. We note that this is a much milder condition than strong monotonicity, used in the current literature. |
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Keywords: | Coerciveness Merit function Complementarity problem Symmetric cone Euclidean Jordan algebra |
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