Abstract.
We consider semidefinite monotone linear complementarity problems (SDLCP) in the space n of real symmetric n×n-matrices equipped with the cone n + of all symmetric positive semidefinite matrices. One may define weighted (using any M∈ n ++ as weight) infeasible interior point paths by replacing the standard condition XY=rI, r>0, (that defines the usual central path) by (XY+YX)/2=rM. Under some mild assumptions (the most stringent is the existence of some strictly complementary solution of (SDLCP)), these paths have a limit as r↓0, and they depend analytically on all path parameters (such as r and M), even at the limit point r=0.
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Mathematics Subject Classification (1991): 90C33, 65K05
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Preiß, M., Stoer, J. Analysis of infeasible-interior-point paths arising with semidefinite linear complementarity problems. Math. Program., Ser. A 99, 499–520 (2004). https://doi.org/10.1007/s10107-003-0463-x
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DOI: https://doi.org/10.1007/s10107-003-0463-x