具有线性不等式约束非线性规划问题的降维算法

对线性约束的一般非线性规划问题进行了研究,在算法中提到的起作用集策略,与常见的起作用集算法相比较;在迭代过程中求解等式约束子问题时采用了降维算法,而对于不等式约束子问题采用了起作用集算法.通过数值试验,说明了算法的有效性.算法对于求解非线性约束非线性规划问题提出了一种新思路,将非线性约束线性化,解决一般此类问题.

Descending Dimension Algorithm of Nolinear Programming Problem with Linear Inequality Constraints

The general nonlinear programming with linear constraints was investigated. In the algorithm, the method of contributing set was used. Comparing with the general contributing set method, the descending dimension method was used to solve the sub-problem with equality constraints in iterative procedure and the problem with inequality constraints. The algorithm is effective by the numerical test. Finally, it was proved that the iteration points are descending, when the objective functions are convex.