NONMONOTONIC TRUST REGION PROJECTED REDUCED HESSIAN ALGORITHM WITH TWO-PIECE UPDATE FOR CONSTRAINED OPTIMIZATION

作     者：ZHUDetong ZHU Detong(Department of Mathematics, Shanghai Normal University, Shanghai 200234, China)

作者机构：DepartmentofMathematicsShanghaiNormalUniversityShanghai200234China 

出 版 物：《Journal of Systems Science & Complexity》 (系统科学与复杂性学报（英文版）)

年 卷 期：2004年第17卷第3期

页      面：332-348页

核心收录：

学科分类：08[工学] 081202[工学-计算机软件与理论] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：The author gratefully acknowledges the partial supports of the National Science Foundation of China Grant (10071050) Science Foundation of Shanghai Technical Sciences Committee Grant (02ZA14070) Science Foundation of Shanghai Education Committee Grant 

主　　题：trust region strategy nonmonotonic technique fletcher's penalty function two-piece update superlinear convergence 

摘      要：This paper proposes a two-piece update of projected reduced Hessian algorithmwith nonmonotonic trust region strategy for solving nonlinear equality constrained optimizationproblems. In order to deal with large problems, a two-piece update of two-side projected reducedHessian is used to replace full Hessian matrix. By adopting the Fletcher s penalty function as themerit function, a nonmonotonic trust region strategy is suggested which does not require the meritfunction to reduce its value in every iteration. The two-piece update of projected reduced Hessianalgorithm which switches to nonmonotonic trust region technique possesses global convergence whilemaintaining a two-step Q-superlinear local convergence rate under some reasonable ***, one step Q-superlinear local convergence rate can be obtained if at least one of theupdate formulas is updated at each iteration by an alternative update rule. The numerical experimentresults are reported to show the effectiveness of the proposed algorithm.