ON THE SOLUTION SET OF GENERALIZED QUASI-HOMOGENEOUS  COMPLEMENTARITY PROBLEMS

Hoàng Kim Chi; Vũ Tuấn Anh; Hoàng Văn Hùng

doi:10.34238/tnu-jst.5337

ON THE SOLUTION SET OF GENERALIZED QUASI-HOMOGENEOUS COMPLEMENTARITY PROBLEMS

About this article

Received: 09/12/21 Revised: 19/04/22 Published: 21/04/22

Authors

1. Hoang Kim Chi , Vietnam Maritime University
2. Vu Tuan Anh, Vietnam Maritime University
3. Hoang Van Hung, Vietnam Maritime University

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.

Keywords

Generalized complementarity problem; p-degree quasi-homogeneous map; Generalized quasi-homogeneous complementarity problem; Exceptionally regular pair of positively homogeneous maps for cone K; Exceptional family of elements for generalized complementar

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DOI: https://doi.org/10.34238/tnu-jst.5337

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