The Alternating Descent Conditional Gradient Method for Sparse Inverse Problems
针对可微观测模型的稀疏逆问题，提出一种结合非凸局部搜索与凸全局条件梯度的混合算法，在超分辨显微镜等应用中取得最优结果。
We propose a variant of the classical conditional gradient method for sparse inverse problems with differentiable observation models. Such models arise in many practical problems including superresolution microscopy, time-series modeling, and matrix completion. Our algorithm combines nonconvex and convex optimization techniques: we propose global conditional gradient steps alternating with nonconvex local search exploiting the differentiable observation model. This hybridization gives the theoretical global optimality guarantees and stopping conditions of convex optimization along with the performance and modeling flexibility associated with nonconvex optimization. Our experiments demonstrate that our technique achieves state-of-the-art results in several applications.