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Vietnam Journal of Mathematics 39:1 (2011) 79-89 

A Characterization of Partition Systems of Rn and Application

Huynh The Phung

Abstract. An m-partition of Rn is, by definition, a system of m + n vectors

U = {u1,0, u1,1, u2,0, u2,1, , um,0, um,1, um+1, , un} Rn,

such that, for every x Rn there exists a unique vector λ sastisfying

λ = (λ1,0, λ1,1, , λm,0, λm,1, λm+1, , λn)T Rm+n,

λi,s 0, (i, s) I S,

λi,0i,1 = 0, i I,

x = + ,

 

where I := {1, 2, , m}, J := {m + 1, , n} and S := {0, 1}.

Systems of this type are usually encountered in linear complementarity problems. By studying them we expect to provide some strong tools for investigating theory of complementarity problems. Specifically, in this paper we shall prove a basic characterization of partition systems in Rn and then derive some direct applications to linear complementarity problems.

2000 Mathematics Subject Classification: 15A15, 90C33.

Keywords: m-partition, complete partition, linear complementarity problem.

 

 

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