A method for convex curve approximation

被引：23
|
作者：
Yang, XQ
Goh, CJ
机构：
[1] Department of Mathematics, University of Western Australia, Nedlands, WA
来源：
EUROPEAN JOURNAL OF OPERATIONAL RESEARCH | 1997年 / 97卷 / 01期
基金：
澳大利亚研究理事会;
关键词：
convex curve; approximation method; quadratic convergence; bi-criteria network program;
D O I：
10.1016/0377-2217(95)00368-1
中图分类号：
C93 [管理学];
学科分类号：
12 ; 1201 ; 1202 ; 120202 ;
摘要：
In this paper, a new sandwich method is introduced to approximate a convex curve in R(2). This method requires only function evaluation and the solution of a number of scalar optimization problems. A quadratic convergence property of the method is established, that is, the total number of optimization problems solved is bounded by a constant multiple of the square root of the inverse of the given error. An application to approximation of the efficient frontier of a bi-criteria convex quadratic network program is given.
引用
收藏
页码：205 / 212
页数：8
相关论文
共 50 条
  • [1] A Novel Iterative Convex Approximation Method
    Yang, Yang
    Pesavento, Marius
    [J]. 2015 IEEE 6TH INTERNATIONAL WORKSHOP ON COMPUTATIONAL ADVANCES IN MULTI-SENSOR ADAPTIVE PROCESSING (CAMSAP), 2015, : 297 - 300
  • [2] CONVEX-SPLINE APPROXIMATION OF A SEISMIC TRAVEL-TIME CURVE
    BURMIN, VY
    [J]. IZVESTIYA AKADEMII NAUK SSSR FIZIKA ZEMLI, 1980, (02): : 90 - 96
  • [3] MONOTONE AND CONVEX APPROXIMATION BY SPLINES - ERROR-ESTIMATES AND A CURVE FITTING ALGORITHM
    BEATSON, RK
    [J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 1982, 19 (06) : 1278 - 1285
  • [4] Inner approximation method for a reverse convex programming problem
    Yamada, S
    Tanino, T
    Inuiguchi, M
    [J]. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2000, 107 (02) : 355 - 389
  • [5] Inner Approximation Method for a Reverse Convex Programming Problem
    S. Yamada
    T. Tanino
    M. Inuiguchi
    [J]. Journal of Optimization Theory and Applications, 2000, 107 : 355 - 389
  • [6] Projection method of approximation gradient for convex programming problems
    Tyulyukin, VA
    [J]. NONSMOOTH AND DISCONTINUOUS PROBLEMS OF CONTROL AND OPTIMIZATION (NDPCO'98), 1999, : 215 - 217
  • [7] Conforming approximation of convex functions with the finite element method
    Wachsmuth, Gerd
    [J]. NUMERISCHE MATHEMATIK, 2017, 137 (03) : 741 - 772
  • [8] Conforming approximation of convex functions with the finite element method
    Gerd Wachsmuth
    [J]. Numerische Mathematik, 2017, 137 : 741 - 772
  • [9] Numerical approximation method for multiscale model of map curve
    Wang, Ping
    Zhou, Chen
    Chen, Wei
    Shen, Wanqiang
    [J]. Proceedings of SPIE - The International Society for Optical Engineering, 2022, 12163
  • [10] AN OUTER APPROXIMATION METHOD FOR MINIMIZING THE PRODUCT OF SEVERAL CONVEX-FUNCTIONS ON A CONVEX SET
    KUNO, T
    YAJIMA, Y
    KONNO, H
    [J]. JOURNAL OF GLOBAL OPTIMIZATION, 1993, 3 (03) : 325 - 335
12345