信赖域内点算法在正定几何规划问题中的应用

摘要

为寻求能够降低正定几何规划问题难度的新方法,本文首先尝试运用对偶理论把正定几何规划问题转化成等式约束和非负约束条件下的非线性规划问题,然后结合信赖域算法和内点算法构造出一种求解正定式几何规划问题的新算法,并在较少条件下证明了该算法的收敛性.该算法一方面减少了计算量,另一方面还可以降低求解几何规划的困难度.%Positive geometric programming is an important part of nonlinear programming.In order to find a new method to reduce the difficulty of positive geometric programming,the positive geometric programming is substited for nonlinear programming with nonnegative constraint and equation constrain by using the duality theory.A new algorithm is constructed by combing trust region algorithm and the interior point algorithm for solving the positive geometric programming.Under mild conditions,the convergence is proved.The method not only decreases the iteration step but also reduces the degrees of difficulty for solving the positive geometric programming.