REDUCTION OF MONOTONE LINEAR COMPLEMENTARITY PROBLEMS OVER CONES TO LINEAR PROGRAMS OVER CONES

Dedicated to Hoang Tuy on the occasion of his seventieth birthday Abstract. This short note presents a constructive way of reducing monotone LCPs (linear complementarity problems) over cones to LPs (li- near programs) over cones. In particular, the monotone semideflnite lin- ear complementarity problem (SDLCP) in symmetric matrices, which was recently proposed by Kojima, Shindoh and Hara, is reducible to an SDP (semideflnite program). This gives a negative answer to their question whether the monotone SDLCP in symmetric matrices is an essential gen- eralization of the SDP.

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