Steepest descent algorithms in a space of measures

被引:24
|
作者
Molchanov, I
Zuyev, S
机构
[1] Univ Glasgow, Dept Stat, Glasgow G12 8QW, Lanark, Scotland
[2] Univ Strathclyde, Dept Stat & Modelling Sci, Glasgow G1 1XH, Lanark, Scotland
关键词
gradient methods; steepest descent; k-means; P-means; optimal experimental design; Poisson process; Boolean model; Splus; R;
D O I
10.1023/A:1014878317736
中图分类号
TP301 [理论、方法];
学科分类号
081202 ;
摘要
The paper describes descent type algorithms suitable for solving optimisation problems for functionals that depend on measures. We mention several examples of such problems that appear in optimal design, cluster analysis and optimisation of spatial distribution of coverage processes.
引用
收藏
页码:115 / 123
页数:9
相关论文
共 50 条
  • [21] METHOD OF STEEPEST DESCENT
    CHAPMAN, PB
    CANADIAN MATHEMATICAL BULLETIN, 1967, 10 (01): : 133 - &
  • [22] HOMING BY STEEPEST DESCENT
    TALKIN, AI
    IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1966, AC11 (01) : 136 - &
  • [23] ALGORITHMS AND ACCURACY REQUIREMENTS FOR COMPUTING REACTION PATHS BY THE METHOD OF STEEPEST DESCENT
    GARRETT, BC
    REDMON, MJ
    STECKLER, R
    TRUHLAR, DG
    BALDRIDGE, KK
    BARTOL, D
    SCHMIDT, MW
    GORDON, MS
    JOURNAL OF PHYSICAL CHEMISTRY, 1988, 92 (06): : 1476 - 1488
  • [24] On the direction of the steepest descent
    Malozemov, V. N.
    Tamasyan, G. Sh
    VESTNIK SANKT-PETERBURGSKOGO UNIVERSITETA SERIYA 10 PRIKLADNAYA MATEMATIKA INFORMATIKA PROTSESSY UPRAVLENIYA, 2019, 15 (04): : 489 - 501
  • [25] ON STABILITY AND STEEPEST DESCENT
    RAJARAMAN, V
    WERTZ, HJ
    IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1963, AC 8 (01) : 61 - &
  • [26] Deterministic Boltzmann Learning Performs Steepest Descent in Weight-Space
    Hinton, Geoffrey E.
    NEURAL COMPUTATION, 1989, 1 (01) : 143 - 150
  • [27] Exact bounds for steepest descent algorithms of L-convex function minimization
    Murota, Kazuo
    Shioura, Akiyoshi
    OPERATIONS RESEARCH LETTERS, 2014, 42 (05) : 361 - 366
  • [28] Iterative algorithms based on the hybrid steepest descent method for the split feasibility problem
    Jung, Jong Soo
    JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS, 2016, 9 (06): : 4214 - 4225
  • [29] Distributed Algorithms for Multicommodity Flow Problems via Approximate Steepest Descent Framework
    Awerbuch, Baruch
    Khandekar, Rohit
    Rao, Satish
    PROCEEDINGS OF THE EIGHTEENTH ANNUAL ACM-SIAM SYMPOSIUM ON DISCRETE ALGORITHMS, 2007, : 949 - +
  • [30] Distributed Algorithms for Multicommodity Flow Problems via Approximate Steepest Descent Framework
    Awerbuch, Baruch
    Khandekar, Rohit
    Rao, Satish
    ACM TRANSACTIONS ON ALGORITHMS, 2012, 9 (01)