Active-Set Identification with Complexity Guarantees of an Almost Cyclic 2-Coordinate Descent Method with Armijo Line Search
研究了一种几乎循环2坐标下降法，用于求解带一个线性耦合约束和简单边界的问题，证明了在非凸和凸条件下主动集的有限步识别，并给出了复杂度结果，对优化算法研究者有用。
This paper establishes finite active-set identification of an almost cyclic 2-coordinate descent method for problems with one linear coupling constraint and simple bounds. First, general active-set identification results are stated for nonconvex objective functions. Then, under convexity and a quadratic growth condition (satisfied by any strongly convex function), complexity results on the number of iterations required to identify the active set are given. In our analysis, a simple Armijo line search is used to compute the stepsize, thus not requiring exact minimizations or additional information.