The Josephy-Newton Method For Semismooth Generalized Equations And The Application Of Abstract Optimization Problem

Basic Josephy-Newton algorithm of the generalized equation was the extension of the Newton algorithm for general variational problem. As its special application. Josephy-Newton algorithm provided a convenient tool for the analysis of sequential quadratic programming optimization problem (SQP) algorithm.This paper studied that a class of optimization problems with cone constraints and the KKT generalized equation. First, with the aid of linearized optimization problem, under the assumption of the nondegeneracy condition, the thesis proved that the second order sufficient condition contained the CD-regularity of the KKT generalized equation for optimization problem. Then, it considered the SQP algo-rithm of the general cone constrained optimization problem and Josephy-Newton algorithm of the corresponding KKT generalized equation. At the same time, it proved that the local convergence of the related Josephy-Newton algorithm. Fi-nally, taking use of the semismooth sequence quadratic programming algorithm to get the necessary condition of the primal superlinear convergence.