Convergence analysis of incremental quasi-subgradient method on Riemannian manifolds with lower bounded curvature

被引：0
|
作者：
Ansari, Qamrul Hasan [1 ,2 ]
Uddin, Moin [1 ]
机构：
[1] Aligarh Muslim Univ, Dept Math, Aligarh, India
[2] Chongqing Univ Technol, Chongqing, Peoples R China
来源：
OPTIMIZATION | 2024年
关键词：
Quasi-convex optimization problems; sum-minimization problems; subgradient method; Greenberg-Pierskalla quasi-subdifferential; Riemannian manifolds; CONVEX FEASIBILITY; ALGORITHMS; SUM;
D O I：
10.1080/02331934.2024.2414782
中图分类号：
C93 [管理学]; O22 [运筹学];
学科分类号：
070105 ; 12 ; 1201 ; 1202 ; 120202 ;
摘要：
We study the convergence analysis of the incremental quasi-subgradient method for solving the sum of geodesic quasi-convex functions on Riemannian manifolds whose sectional curvature is bounded below. The convergence result of the method with diminishing stepsize is established. An application of the studied algorithm to the sum of ratio problems in the setting of Riemannian manifolds with negative sectional curvature is given.
引用
收藏
页数：20
相关论文
共 50 条
  • [1] Incremental Quasi-Subgradient Method for Minimizing Sum of Geodesic Quasi-Convex Functions on Riemannian Manifolds with Applications
    Ansari, Qamrul Hasan
    Babu, Feeroz
    Zeeshan, Mohd
    NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2021, 42 (13) : 1492 - 1521
  • [2] Iteration-complexity of the subgradient method on Riemannian manifolds with lower bounded curvature
    Ferreira, O. P.
    Louzeiro, M. S.
    Prudente, L. F.
    OPTIMIZATION, 2019, 68 (04) : 713 - 729
  • [3] An Incremental Subgradient Method on Riemannian Manifolds
    Zhang, Peng
    Bao, Gejun
    JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2018, 176 (03) : 711 - 727
  • [4] An Incremental Subgradient Method on Riemannian Manifolds
    Peng Zhang
    Gejun Bao
    Journal of Optimization Theory and Applications, 2018, 176 : 711 - 727
  • [5] Subgradient algorithms on Riemannian manifolds of lower bounded curvatures
    Wang, X. M.
    OPTIMIZATION, 2018, 67 (01) : 179 - 194
  • [6] GRADIENT METHOD FOR OPTIMIZATION ON RIEMANNIAN MANIFOLDS WITH LOWER BOUNDED CURVATURE
    Ferreira, O. P.
    Louzeiro, M. S.
    Prudente, L. F.
    SIAM JOURNAL ON OPTIMIZATION, 2019, 29 (04) : 2517 - 2541
  • [7] Subgradient Projection Algorithms for Convex Feasibility on Riemannian Manifolds with Lower Bounded Curvatures
    Wang, X. M.
    Li, C.
    Yao, J. C.
    JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2015, 164 (01) : 202 - 217
  • [8] Incremental quasi-subgradient methods for minimizing the sum of quasi-convex functions
    Hu, Yaohua
    Yu, Carisa Kwok Wai
    Yang, Xiaoqi
    JOURNAL OF GLOBAL OPTIMIZATION, 2019, 75 (04) : 1003 - 1028
  • [9] Subgradient Projection Algorithms for Convex Feasibility on Riemannian Manifolds with Lower Bounded Curvatures
    X. M. Wang
    C. Li
    J. C. Yao
    Journal of Optimization Theory and Applications, 2015, 164 : 202 - 217
  • [10] Incremental quasi-subgradient methods for minimizing the sum of quasi-convex functions
    Yaohua Hu
    Carisa Kwok Wai Yu
    Xiaoqi Yang
    Journal of Global Optimization, 2019, 75 : 1003 - 1028
12345