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关于补几何规划算法的收敛性

崔晋川,吴方   

  1. 中国科学院应用数学研究所 ,中国科学院应用数学研究所
  • 出版日期:1983-04-14 发布日期:1983-04-14

崔晋川,吴方. 关于补几何规划算法的收敛性[J]. 计算数学, 1983, 5(4): 412-420.

ON THE CONVERGENCE PROPERTY OF AN ALGORITHM FOR THE COMPLEMENTARY GEOMETRIC PROGRAMMING

  1. Cui Jin-chuan;Wu Fang Institute of Applied Mathematic, Academia Sinica
  • Online:1983-04-14 Published:1983-04-14
几何规划是非线性规划的一个分支. Zener,Duffin与Peterson最初以几何平均≤算术平均这一著名的不等式为基础发展了一套研究正项几何规划
For the solution of the standard complementary geometric programming min x1, (1) s. t. p_m(x)/Q_m(x)≤1 (m = 1,2,…,M) x > 0where P_m(x) and Q_m(x)(m = 1, 2,…, M) are all posynomials of x = (x_1,…,x_n)~T, analgorithm was given in [6]. Let x~* be any limit point of the point sequence generated bythis algorithm, by assuming that one certain posynomial geometric programming associated withx~* is superconsistent, we prove that x~* is a Kuhn-Tucker point of (1).
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[1] R. J. Duffin, E. L. Peterson, C. M. Zener, Geometric Programming. John Wiley, New York, 1967.
[2] U. Passy,D. J. Wilde. Generalized polynomial optimizations,SIAM J. Appl. Math., 15(1967) ,1344--1356.
[3] G. E. Blau, D. J. Wilde, Generalized polynomial programmig, Canad. J.Chemical Engineering, 47(1969) , 317-326.
[4] O. J. Wilde, G. S, Beightler, Foundations of Optimization. prentice-Hall, Englewood Cliffs, NJ.1967.
[5] R. J. Duffin, E. L. Peterson. Reversed geometric programming.treated by harmonic medns, Indiana Univ. Math. J., 22(1972) , 531-550.
[6] M. Avriel, A. C. Williams, Complementary geometric programming, SIAM J. Appl. Math., 19(1970) , 125--141.
[7] J. G. Ecker, Geometric Programming: Computations and Applications, SIAM REVIEW., 22(1980) ,338--362.
[8] 吴方,袁云耀,几何规划,数学的实践与认识,1,4,1982.
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