A Copositivity-type Existence Result for Weakly Homogeneous Variational Inequalities

Recently, Gowda and Sossa [Math. Program., 2019, 177: 149–171] studied the existence of solutions to weakly homogeneous variational inequalities. In particular, their main result, based on a degree-theoretic condition and a constraint on the corresponding cone complementarity problem, covers a majority of existence results on the subcategory problems of weakly homogeneous variational inequalities. In this paper, what we achieve is a new copositivity-type existence result for the weakly homogeneous variational inequality. The conditions we used are easier to check than the degree-theoretic condition and our result crosses each other with the main result established by Gowda and Sossa and the main result given by Ma, Zheng and Huang [SIAM J. Optim., 2020, 30(1): 132–148], respectively. Besides, we show the distinctiveness of our existence result by comparing it with the well-known coercivity result obtained for variational inequalities and a norm-coercivity result obtained for complementarity problems, respectively.