ON THE SOLUTION SET OF GENERALIZED QUASI-HOMOGENEOUS COMPLEMENTARITY PROBLEMS

Abstract

This paper investigates the properties of the solution set for generalized quasi-homogeneous  complementarity  problems. The authors  introduce  the concept of  p-degree quasi-homogeneous  maps with p>0. Using the concepts of exceptionally regular pair of positively homogeneous  maps  for cone K, exceptional  family of  elements  for generalized complementarity problems  and  the properties of p-degree quasi-homogeneous  maps, the authors  proved  a sufficient condition  for compactness and non-emptiness of the solution set for generalized quasi-homogeneous  complementarity  problems. The class of p-degree quasi-homogeneous maps with p>0 properly contains the class of polynomial maps. So, the obtained result is better  a  result  of  L.Ling, C.Ling, H.He [Pac. J. Optim, 16(1) 155-174, 2020.] about the properties of the solution set for generalized polynomial  complementarity  problems.