The continuous stochastic gradient method: part II–application and numerics
分析了连续随机梯度法的数值表现，包括拓扑优化应用和收敛速度估计。该方法混合随机与全梯度策略，能解决变量多、目标函数含非线性多重积分的问题，对优化算法研究者有用。
Abstract In this contribution, we present a numerical analysis of the continuous stochastic gradient (CSG) method, including applications from topology optimization and convergence rates. In contrast to standard stochastic gradient optimization schemes, CSG does not discard old gradient samples from previous iterations. Instead, design dependent integration weights are calculated to form a convex combination as an approximation to the true gradient at the current design. As the approximation error vanishes in the course of the iterations, CSG represents a hybrid approach, starting off like a purely stochastic method and behaving like a full gradient scheme in the limit. In this work, the efficiency of CSG is demonstrated for practically relevant applications from topology optimization. These settings are characterized by both, a large number of optimization variables and an objective function, whose evaluation requires the numerical computation of multiple integrals concatenated in a nonlinear fashion. Such problems could not be solved by any existing optimization method before. Lastly, with regards to convergence rates, first estimates are provided and confirmed with the help of numerical experiments.