正定式约束下广义几何规划的一种线性化方法

A New Linearization Method for Posynomial Constrained Generalized Geometric Programming

几何规划是一类具有特殊形式的非线性规划问题,正定式几何规划问题借助于凸规划问题的求解已基本得到解决.但广义几何规划问题作为一种特殊的(DC)规划,至今没有好的求解方法.利用线性化技术,将正定式约束下的一类广义几何规划问题转化为一列凸规划问题进行求解,构造了正定式约束下广义几何规划的一种新算法,并证明了该算法的全局收敛性.

Geometric programming was a type of nonlinear programming problem in special form. A posy- nomial geometric programming could be converted to convex programming problem. Therefore, the prob- lem of posynomial geometric programming could be solved just like that of convex program. But general- ized geometric programming was a special DC programming, and its problem was very difficult to solve. And so far, there were not any good methods for this problem. By using linearization technique, posyno- mial ct,nstrained generalized geometric programming was converted to a sequence of convex programming, and a new algorithm was proposed the problem of posynomial constrained generalized geometric program- ming. The proof of global convergence of the proposed algorithm was also given.