Stability of the Asymptotic Behavior for Continuous Descent Methods with a Convex Objective Function

被引:0
|
作者
Zaslavski, Alexander J. [1 ]
机构
[1] Technion Israel Inst Technol, Dept Math, Haifa, Israel
来源
MINIMAX THEORY AND ITS APPLICATIONS | 2024年 / 9卷 / 02期
关键词
Banach space; complete metric space; convex function; descent method; regular vector field; CONVERGENCE; OPTIMIZATION; PROJECTION;
D O I
暂无
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We study continuous descent methods for the minimization of a convex objective function and obtain convergence results for those methods which are generated by approximations of regular vector fields. These results improve convergence results known in the literature.
引用
收藏
页码:421 / 432
页数:12
相关论文
共 50 条
  • [21] Convergence of the steepest descent method with line searches and uniformly convex objective in reflexive Banach spaces
    Gallego, Fernando Andres
    Quintero, John Jairo
    Riano, Juan Carlos
    MATHEMATICAL COMMUNICATIONS, 2015, 20 (02) : 161 - 173
  • [22] On perturbed steepest descent methods with inexact line search for bilevel convex optimization
    Helou Neto, Elias Salomao
    De Pierro, Alvaro Rodolfo
    OPTIMIZATION, 2011, 60 (8-9) : 991 - 1008
  • [23] Asymptotic Behavior of Solutions to a Second-Order Gradient Equation of Pseudo-Convex Type
    Khatibzadeh, Hadi
    Morosanu, Gheorghe
    JOURNAL OF CONVEX ANALYSIS, 2019, 26 (04) : 1175 - 1186
  • [24] Iteration complexity of randomized block-coordinate descent methods for minimizing a composite function
    Richtarik, Peter
    Takac, Martin
    MATHEMATICAL PROGRAMMING, 2014, 144 (1-2) : 1 - 38
  • [25] From error bounds to the complexity of first-order descent methods for convex functions
    Bolte, Jerome
    Trong Phong Nguyen
    Peypouquet, Juan
    Suter, Bruce W.
    MATHEMATICAL PROGRAMMING, 2017, 165 (02) : 471 - 507
  • [26] M-CONVEX FUNCTION MINIMIZATION BY CONTINUOUS RELAXATION APPROACH: PROXIMITY THEOREM AND ALGORITHM
    Moriguchi, Satoko
    Shioura, Akiyoshi
    Tsuchimura, Nobuyuki
    SIAM JOURNAL ON OPTIMIZATION, 2011, 21 (03) : 633 - 668
  • [27] Applications of convex analysis to consensus algorithms, pointwise asymptotic stability, and its robustness
    Goebel, Rafal
    Sanfelice, Ricardo G.
    2018 IEEE CONFERENCE ON DECISION AND CONTROL (CDC), 2018, : 2378 - 2383
  • [28] Asymptotic Behavior of Resolvents of a Convergent Sequence of Convex Functions on Complete Geodesic Spaces
    Kimura, Yasunori
    Shindo, Keisuke
    AXIOMS, 2022, 11 (01)
  • [29] ON THE STABILITY AND ASYMPTOTIC BEHAVIOR FOR A QUASI-LINEAR PARABOLIC FLOW
    Ma, L., I
    Shi, Z. I. Z. H. E. N.
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, 2024, 17 (02): : 620 - 633
  • [30] DISCRETE L-CONVEX FUNCTION MINIMIZATION BASED ON CONTINUOUS RELAXATION
    Moriguchi, Satoko
    Tsuchimura, Nobuyuki
    PACIFIC JOURNAL OF OPTIMIZATION, 2009, 5 (02): : 227 - 236