Projection free methods on product domains
研究了乘积域上的无投影块坐标方法，填补了经典Frank-Wolfe理论与块坐标情形之间的理论空白，并扩展到非凸情形，通过新的收敛理论和主动集识别结果有效利用解的稀疏性。
Abstract Projection-free block-coordinate methods avoid high computational cost per iteration, and at the same time exploit the particular problem structure of product domains. Frank–Wolfe-like approaches rank among the most popular ones of this type. However, as observed in the literature, there was a gap between the classical Frank–Wolfe theory and the block-coordinate case, with no guarantees of linear convergence rates even for strongly convex objectives in the latter. Moreover, most of previous research concentrated on convex objectives. This study now deals also with the non-convex case and reduces above-mentioned theory gap, in combining a new, fully developed convergence theory with novel active set identification results which ensure that inherent sparsity of solutions can be exploited in an efficient way. Preliminary numerical experiments seem to justify our approach and also show promising results for obtaining global solutions in the non-convex case.