解不等式约束问题的不可行SSLE滤子算法

An Infeasible SSLE Filter Algorithm for Inequality Constrained Optimization

摘要:

考虑将原不等式约束优化问题转化为与其等价的带等式约束的优化问题，并证明它们具有相同的KKT条件.转化后的问题要求其乘子是非负的，故其KKT条件与一般的等式约束优化问题不同. 针对这种具有特定的等式约束优化问题，提出了一种求解不等式约束优化问题的不可行序列线性规划滤子方法.该算法只需求解两个具有相同系数矩阵的线性方程组以得到搜索方向，因此计算量较小.最后给出了该算法的全局收敛性证明和数值结果.

关键词:序列线性方程组; 滤子; 线搜索; 非线性约束优化

Abstract:

The inequality constrained optimization problem is reformulated as its equivalent equality constrained optimization problem.It is proved that they have the same KarushKuhnTucker(KKT) conditions under some suitable conditions.The multiplier of the equivalent equality constrained optimization problem needs to be nonnegative.Therefore,its KKT conditions are different from those of the general equality constrained optimization problem.An infeasible sequential system of linear equations(SSLE) filter algorithm is presented to solve this type of problem.It only needs to solve two systems of linear equations with the same nonsingular coefficient matrix,which results in a less computation.The global convergence of the algorithm is established under suitable conditions.Some numerical results are also reported.

Key words:sequential systems of linear equations; filter; line search; inequality constrained optimization