Abstract:

An exceptional family of elements were constructed for the P₀ horizonal linear complementarity problem with the equivalent formula of the complementarity problem, an alternative theorem of P₀horizonal linear complementarity problem with a solution was established, and the solvability of it under the condition of  Mx+Ny=0, x≥0, y≥0, x^Ty=0 has unique zero solution was obtained by using this alternative theorem.

Key words: horizonal linear complementarity problem, exceptional family of elements, P₀matrix pair