论文标题
凸混合构成优化与弗兰克·沃尔夫方法
Convex mixed-integer optimization with Frank-Wolfe methods
论文作者
论文摘要
混合成员非线性优化包括一系列既带来理论和计算挑战的广泛问题。我们提出了一种基于带有凸节点松弛的分支和结合算法来解决这些问题的新方法。这些放松是通过混合构成可行点的凸壳上的Frank-Wolfe算法来解决的，而不是通过呼叫混合构成线性求解器作为线性最小化的Oracle的连续放松。所提出的方法在处理多面体约束的单个表示时计算可行的解决方案，利用混合构成线性求解器的全部范围而无需外部近似方案，并且可以利用节点子问题的不精确溶液。
Mixed-integer nonlinear optimization encompasses a broad class of problems that present both theoretical and computational challenges. We propose a new type of method to solve these problems based on a branch-and-bound algorithm with convex node relaxations. These relaxations are solved with a Frank-Wolfe algorithm over the convex hull of mixed-integer feasible points instead of the continuous relaxation via calls to a mixed-integer linear solver as the linear minimization oracle. The proposed method computes feasible solutions while working on a single representation of the polyhedral constraints, leveraging the full extent of mixed-integer linear solvers without an outer approximation scheme and can exploit inexact solutions of node subproblems.
