论文标题
螺旋：非凸有限和最小化的超级线性收敛增量近端算法
SPIRAL: A superlinearly convergent incremental proximal algorithm for nonconvex finite sum minimization
论文作者
论文摘要
我们引入了螺旋（一种超线性收敛的增量近端算法），用于在相对平滑度假设下求解非凸的正则有限和问题。螺旋的每一个迭代都由一个内部和外环组成。它将增量梯度更新与线条搜索相结合，该线路搜索具有非渐近触发的非凡属性，从而在极限点处于轻度假设下，导致超线性收敛。 L-BFGS方向在不同的凸，非凸和非lipschitz可区分问题上的仿真结果表明，我们的算法以及其自适应变体对技术的状态具有竞争力。
We introduce SPIRAL, a SuPerlinearly convergent Incremental pRoximal ALgorithm, for solving nonconvex regularized finite sum problems under a relative smoothness assumption. Each iteration of SPIRAL consists of an inner and an outer loop. It combines incremental gradient updates with a linesearch that has the remarkable property of never being triggered asymptotically, leading to superlinear convergence under mild assumptions at the limit point. Simulation results with L-BFGS directions on different convex, nonconvex, and non-Lipschitz differentiable problems show that our algorithm, as well as its adaptive variant, are competitive to the state of the art.
