求解一类非凸变分不等式的近似点算法
On a Proximal Point Algorithm for Solving a Class of Nonconvex Variational Inequalities
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摘要: 介绍和考虑了一类新的非凸变分不等式，这类变分不等式包括了一些已知的和新的非凸变分不等式作为特例。利用一致 r 近似正规集的概念，建立了这类变分不等式和不动点问题的等价关系。利用该等价关系，给出了一个求解此类非凸变分不等式的近似点算法，并证明了该算法在适当的条件下收敛。Abstract: T his paper introduces and considers a new class of nonconvex variational inequalities .T his class of variational inequalities includes some know n and new nonconvex variational inequalities as special cases . Relying on the γ‐prox‐regularity notion ,we have established the equivalence between the variational ine‐qualities and the fixed point problems .By means of the equivalence ,we suggest and analyze a proximal point algorithm for solving this nonconvex variational inequalities .The new algorithm converges under certain mild conditions .As a consequence ,the algorithm and results presented in the paper overcome incor‐rect algorithms and results existing in the literature [1] .Our results can also be viewed as a novel and im‐portant extension and improvement of the previously known results .
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