On a Proximal Point Algorithm for Solving a Class of Nonconvex Variational Inequalities

Key words: 
• nonconvex variational inequalities，uniformly prox-regular sets，strongly monotonicity，projec-tion technique /
•  /
•  /

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 .