一种松懈的梯度投影算法

A RELAXED GRADIENT PROJECTION METHOD

结合ＧＬＰ投影梯度法，提出一种解一般凸规划问题的外点迈近算法，在适当条件下证明了收敛性定理。此算法较之其它外点法的优点，在于其子问题的约束集合不是递增的。即：算法在每次迭代解一个二次规划问题，这个二次规划问题的约束条件只依赖于最优解的当前估计，并且该算法的计算复杂性比ＧＬＰ投影梯度法大大减少。

In this paper,a new outer approximation algorithm for solving general convexprograms with GLP Gradient Projection method is provided,and the convergence under properconditions is proved.The advantage of the algorithm is that the approximation of the constraintset is not cunmulative. That is,the algorithm solves at each iteration a quadratic program whoseconstrains depend only on the current estimate of an optimal solution.