Hilbert空间中伪单调变分不等式的严格可行性

Strict Feasi bility of Pseudo-monotone Variational Inequality in Hilbert Spaces

文章在映射为全连续场和伪单调的情况下,运用拓扑度的同伦不变性,切除性等性质,证明了在Hilbret空间中变分不等式解的非空有界性等价于严格可行性,将已有的结果从有限维欧式空间推广到了无穷维的Hilbret空间中。

This paper proves that solution set of variational inequality being nonempty and bounded is equivalent to the strict feasibility in Hibert spaces. We provide that the mapping is a compact field and pseudo-monotone, and use the homotopy invariance of the topological degree and the excision property of the topological degree. This generalizes some known results from finite dimensional spaces to infinite dimensional spaces.