一种单位化的增量梯度算法

研究目标函数是若干光滑函数和的可分离优化问题，提出了一种单位化增量梯度算法。该算法每次子迭代只需要计算一个（或几个）分量函数的单位负梯度方向作为迭代方向。在一定条件下，证明了采用发散步长的单位化增量梯度算法的收敛性。作为应用，新算法和Bertsekas D P，Tsitsikils J N提出的（没有单位化）增量梯度算法分别用来求解稳健估计问题和源定位问题。数值例子表明，新算法优于（没有单位化）增量梯度算法。

A scaled incremental gradient method

A scaled incremental gradient algorithm for minimizing a sum of continuously differentiable functions is presented. At each iteration of the algorithm, the iterate is updated incrementally by a sequence of some steps, and each step is cyclically evaluates a normalized gradient of a single component function (or several component functions). Under some moderate assumptions, the convergence result of the algorithm employing the divergence step sizes is established. As applications, the new algorithm and the (unscaled) one proposed by Bertsekas D P, Tsitsikils J N are applied to solve the robust estimation problem and the source localization problem, respectively. Some numerical experiments show that the new algorithm is more effective and robust than the corresponding (unscaled) one.