论文标题
一种自适应块Bregman近端梯度方法，用于计算多组分相位晶体模型的固定状态
An adaptive block Bregman proximal gradient method for computing stationary states of multicomponent phase-field crystal model
论文作者
论文摘要
在本文中，我们通过将其作为块约束最小化问题制定来计算多组分相位晶体模型的固定状态。在适当的空间离散化后，原始的无限二二维最小化问题是通过有限维约束的非凸最小化问题近似的。为了有效解决上述优化问题，我们提出了一种所谓的自适应块Bregman近端梯度（AB-BPG）算法，该算法充分利用了问题的块结构。所提出的方法会更新每个订单参数，并且可以以确定性或随机的方式选择块的更新顺序。此外，我们通过开发实用的线性搜索方法选择步骤大小，以使生成的序列可以保持能量耗散，或者随着能量耗散而具有可控的子序列。该方法的收敛性能是建立的，而无需使用Bregman Divergence使用Bulk Energy部分的全局Lipschitz连续性。计算二进制，三元和quinary组件耦合模式Swift-Hohenberg模型中计算固定有序结构的数值结果显示出了许多现有方法的显着加速度。
In this paper, we compute the stationary states of the multicomponent phase-field crystal model by formulating it as a block constrained minimization problem. The original infinite-dimensional non-convex minimization problem is approximated by a finite-dimensional constrained non-convex minimization problem after an appropriate spatial discretization. To efficiently solve the above optimization problem, we propose a so-called adaptive block Bregman proximal gradient (AB-BPG) algorithm that fully exploits the problem's block structure. The proposed method updates each order parameter alternatively, and the update order of blocks can be chosen in a deterministic or random manner. Besides, we choose the step size by developing a practical linear search approach such that the generated sequence either keeps energy dissipation or has a controllable subsequence with energy dissipation. The convergence property of the proposed method is established without the requirement of global Lipschitz continuity of the derivative of the bulk energy part by using the Bregman divergence. The numerical results on computing stationary ordered structures in binary, ternary, and quinary component coupled-mode Swift-Hohenberg models have shown a significant acceleration over many existing methods.
