一个正定几何规划的对偶算法及收敛性

由于正定几何规划的对偶规划只含线性等式约束和非负约束,处理起来似乎要方便得多.然而,实际上许多对偶算法实施起来却往往失败(见2,8,9]),这是由于对偶规划所特有的“块性质”以及目标函数在某些点的不可微性质引起的.因此,近年来主要的努力集中在克服这二个困难上。主要的工作有:1975年Beck和Ecker的修正凹单纯形

AN ALGORITHM FOR DUAL POLYNOMIAL GEOMETRIC PROGRAMMING

In this paper, we present an algorithm of polynomial geometric programming by use ofdual optimal Lagrange multipliers and Hession of dual objective function V (Y, X). The cri-teria for a block of dual variables to move to or away from zero are given. By means of theanti-zigzagging technique we show the convergence of the algorithm. A code of initial solu-tion based on the Linear simplex method is provided. Some preliminary numerical resultsare included for the comparison of the proposed method with the modified reduced gradientmethod in 3].