2 research outputs found
An existence result for weakly homogeneous variational inequalities
In this paper, what we concern about is the weakly homogeneous variational
inequality over a finite dimensional real Hilbert space. We achieve an
existence result {under} copositivity of leading term of the involved map,
norm-coercivity of the natural map and several additional conditions. These
conditions we used are easier to check and cross each other with those utilized
in the main result established by Gowda and Sossa (Math Program 177:149-171,
2019). As a corollary, we obtain a result on the solvability of nonlinear
equations with weakly homogeneous maps involved. Our result enriches the theory
for weakly homogeneous variational inequalities and its subcategory problems in
the sense that the main result established by Gowda and Sossa covers a majority
of existence results on the subcategory problems of weakly homogeneous
variational inequalities. Besides, we compare our {existence} result with the
well-known coercivity result obtained for general variational inequalities and
a norm-coercivity result obtained for general complementarity problems,
respectively
Inexact Newton Method for M-Tensor Equations
We first investigate properties of M-tensor equations. In particular, we show
that if the constant term of the equation is nonnegative, then finding a
nonnegative solution of the equation can be done by finding a positive solution
of a lower dimensional M-tensor equation. We then propose an inexact Newton
method to find a positive solution to the lower dimensional equation and
establish its global convergence. We also show that the convergence rate of the
method is quadratic. At last, we do numerical experiments to test the proposed
Newton method. The results show that the proposed Newton method has a very good
numerical performance