基于增广Lagrange函数的等式约束优化算法

等式约束优化问题是一类比较常见的也是比较简单的约束优化问题,通过研究带有等式约束的优化问题,提出了一个基于增广Lagrange函数的新算法.在新算法中将增广Lagrange函数作为价值函数,将约束优化问题转化为无约束优化问题,用无约束优化方法去解决等式约束优化问题.算法中每一步迭代只需求解一个简单的线性方程组,不需要太大的计算量就可以找到下降方向.算法中初始点是任意的,在适当条件下保证避免罚因子趋于无穷,可以证明算法全局收敛于原问题的KKT点.

An algorithm based on the augmented Lagrange for equality constrained optimization

Equality constrained optimization is the common and easy constrained optimization.A new algorithm based on the augmented Lagrange is proposed by studying equality constrained optimization problems.In the new algorithm,we employ the augmented Lagrange as a merit function and change equality constrained optimization into non-constrained optimization.It can be solved by non-constrained optimization methods.In each iteration the descent direction can be obtained by only calculating a linear system.The initial point is at random.Under suitable conditions,the penalty parameter tends to finite and the algorithm is proved to be globally convergent.