Study On The Projection-Contraction Algorithms For Solving Co-Coercive Variational Inequalities

This thesis studies the projection and contraction algorithms for solving co-coercive variational inequalities.A unified framework of projection and contraction algorithms is given in which the selection of step size rules and the construction of descent directions are analysized. Three fundamental inequalities and some combinations used to constructing descent directions are summarized.Based on the above work, a self-adaptive projection algorithm for solving co-coercive variational inequalities is presented. The estimation of the co-coercive modulus is avoided in the algorithm and the step size is bounded below away from zero. The global conver-gence of the algorithm is obtained easily. In particular, for the box-constrained case, a new descent direction is derived along which a better correction step size can be ob-tained. Meanwhile, in order to make the method implementable, the relationship between the basic and the optimal correction step size is established.As a numerical example, an economic equilibrium problem with bi-level program-ming structure was carried out, the numerical result show the algorithm is efficient.