Weak Sharp Minima Analysis And Strong Convergence Of Algorithm For Equilibrium Problems

Because it contains the breadth and profundity of problems, various types of equilibriumproblems get a deep and wide range of research recently. On the one hand，this dissertation isdevoted to study weak sharp minima and linear separation for vector equilibrium problems; Onthe other hand, we introduce an iterative algorithm for the corresponding scalar equilibriumproblem, and the strong convergence of the algorithm is proved. The main results may besummarized as follows:In chapter2,vector equilibrium problems with matrix inequality constraints are investigatedby using the image space analysis, and linear separation for VEP with matrix inequalityconstraints is characterized. Under the conditions of lipschiz continue and relaxed(γ，r)-cocoercive, the solutions set of the VEP with matrix inequality constraints is characterized by theweak sharp minimum for a certain particular function. This is the extention of the condition ofstrong monotonicity.In chapter3, this dissertation introduces a new iterative scheme for finding a commonelement of the set of solutions of an equilibrium problem, and the set of solutions of thevariational inequality with α-inverse-strongly monotone and the set of common fixed point in aHilbert space. Then, the strong convergence of iterative algorithm is proved under someparameter controlling conditions.