Active-Set Identification with Complexity Guarantees of an Almost Cyclic 2-Coordinate Descent Method with Armijo Line Search

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 results are stated nonconvex objective functions. Then, under convexity a quadratic growth condition (satisfied by any strongly convex function), complexity on the number iterations required to identify active set given. In our analysis, Armijo line search is used compute stepsize, thus not requiring exact minimizations or additional information.