• 论文 •

### 关于补几何规划算法的收敛性

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

### 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

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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