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.

翻译：在本文中, 我们通过将多构件相位晶体模型的固定状态编成一个限制最小化的块状问题来计算多构件相位场晶体模型的固定状态。 原始的无限维非convex 最小化问题在适当的空间分解后被一个有限维度非convex 最小化问题所近似。 为了有效解决上述优化问题, 我们提议了一个所谓的适应性块块Bregman proximal 梯度(AB-BPG)算法, 充分利用问题块状结构。 拟议的方法可以对每个订单参数进行更新, 并且可以以确定或随机的方式选择区块的更新顺序。 此外, 我们通过开发实用的线性搜索方法来选择步骤大小, 这样产生的序列要么保持能量消散, 要么具有可控的子序列与能量消散的亚序列。 在不要求利用布雷格曼差分法确定大能量部分衍生物的全球利普什兹连续性的情况下, 方法的趋同性特性。 。 在二进制、 和四分形形成形成形成结构中计算的固定结构的数值结果,, 显示许多的加速式Swad- sy- swaftide- homety- home- homet- homet- homestmet- homet- homet- homet- homet- homes 方法显示 已经展示了一种显著的多重式 方法。