Abstract
In this paper, we propose a new set of unbounded conditions to make the interior path following method able to solve fixed point problems with both inequality and equality constraints in a class of unbounded nonconvex set. Under suitable assumptions, we give a constructive proof of the existence of interior path leading to the solution point of this class of fixed point problems.
Highlights
1 Introduction It is well known that fixed point theorems have been widely applied to many areas such as mechanics, physics, transportation, control, economics, and optimization
In, Yu and Lin [ ] proposed a homotopy interior path following method to complete this work on a class of nonconvex subset satisfying the normal cone condition, which is a generalization of the convexity
In [ ], by introducing C mappings α(x) = (α (x), . . . , αm(x)) ∈ Rn×m and β(x) = (β (x), . . . , βl(x)) ∈ Rn×l, we further extended the results in [ ] to more general nonconvex sets with both inequality and equality constraint functions
Summary
It is well known that fixed point theorems have been widely applied to many areas such as mechanics, physics, transportation, control, economics, and optimization. In , Yu and Lin [ ] proposed a homotopy interior path following method to complete this work on a class of nonconvex subset satisfying the normal cone condition, which is a generalization of the convexity.
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