SUPERLINEAR CONVERGENCE OF A SEMISMOOTH NEWTON METHOD FOR SOME OPTIMIZATION PROBLEMS WITH APPLICATIONS TO CONTROL THEORY*

被引：0
|
作者：
Departmento de Matemática Aplicada y Ciencias de la Computación, E.T.S.I. Industriales y de Telecomunicación, Universidad de Cantabria, Santander [1 ]
39005, Spain
机构：
来源：
SIAM J. Optim. | / 4卷 / 3681-3698期
关键词：
Newton-Raphson method;
D O I：
10.1137/24M1644286
中图分类号：
学科分类号：
摘要：
In this paper, we formulate a semismooth Newton method for an abstract optimization problem and prove its superlinear convergence by assuming that the no-gap second order sufficient optimality condition and the strict complementarity condition are fulfilled at the local minimizer. Many control problems fit this abstract formulation. In particular, we apply this abstract result to distributed control problems of a semilinear elliptic equation, to boundary bilinear control problems associated with a semilinear elliptic equation, and to distributed control of a semilinear parabolic equation. © 2024 Society for Industrial and Applied Mathematics.
引用
收藏
页码：3681 / 3698
相关论文
共 50 条
  • [21] A feasible semismooth asymptotically Newton method for mixed complementarity problems
    Sun, DF
    Womersley, RS
    Qi, HD
    MATHEMATICAL PROGRAMMING, 2002, 94 (01) : 167 - 187
  • [22] On the Solution of Contact Problems with Tresca Friction by the Semismooth* Newton Method
    Gfrerer, Helmut
    Outrata, Jiri V.
    Valdman, Jan
    LARGE-SCALE SCIENTIFIC COMPUTING (LSSC 2021), 2022, 13127 : 515 - 523
  • [23] A feasible semismooth asymptotically Newton method for mixed complementarity problems
    Defeng Sun
    Robert S. Womersley
    Houduo Qi
    Mathematical Programming, 2002, 94 : 167 - 187
  • [24] A monotone semismooth Newton type method for a class of complementarity problems
    Sun, Zhe
    Zeng, Jinping
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2011, 235 (05) : 1261 - 1274
  • [25] An adaptive semismooth Newton method for approximately solving control-constrained elliptic optimal control problems
    Fard, Omid Solaymani
    Borzabadi, Akbar Hashemi
    Sarani, Farhad
    TRANSACTIONS OF THE INSTITUTE OF MEASUREMENT AND CONTROL, 2019, 41 (11) : 3010 - 3020
  • [26] A damped semismooth Newton method for mixed linear complementarity problems
    Sun, Zhe
    Zeng, Jinping
    OPTIMIZATION METHODS & SOFTWARE, 2011, 26 (02): : 187 - 205
  • [27] Inexact Newton methods for semismooth equations with applications to variational inequality problems
    Facchinei, F
    Fischer, A
    Kanzow, C
    NONLINEAR OPTIMIZATION AND APPLICATIONS, 1996, : 125 - 139
  • [28] Finding global solutions of some inverse optimal control problems using penalization and semismooth Newton methods
    Friedemann, Markus
    Harder, Felix
    Wachsmuth, Gerd
    JOURNAL OF GLOBAL OPTIMIZATION, 2023, 86 (04) : 1025 - 1061
  • [29] An efficient semismooth Newton method for adaptive sparse signal recovery problems
    Ding, Yanyun
    Zhang, Haibin
    Li, Peili
    Xiao, Yunhai
    OPTIMIZATION METHODS & SOFTWARE, 2023, 38 (02): : 262 - 288
  • [30] Feasible Semismooth Newton Method for a Class of Stochastic Linear Complementarity Problems
    G. L. Zhou
    L. Caccetta
    Journal of Optimization Theory and Applications, 2008, 139
12345