SIAM Journal on Optimization, Volume 31, Issue 1, Page 686-701, January 2021.
We consider a linear problem over a finite set of integer vectors and assume that there is a verification oracle, which is an algorithm being able to verify whether a given vector optimizes a given linear function over the feasible set. Given an initial solution, the algorithm proposed in this paper finds an optimal solution of the problem together with a path, in the 1-skeleton of the convex hull of the feasible set, from the initial solution to the optimal solution found. The length of this path is bounded by the sum of distinct values which can be taken by the components of feasible solutions, minus the dimension of the problem. In particular, in the case when the feasible set is a set of binary vectors, the length of the constructed path is bounded by the number of variables, independently of the objective function.

中文翻译：

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验证Oracle给出的整数问题的通用单纯形方法

SIAM优化杂志，第31卷，第1期，第686-701页，2021年1月。
我们考虑有限整数集向量上的线性问题，并假设存在一个验证预言，这是一种能够验证给定向量是否在可行集上优化给定线性函数的算法。给定一个初始解，本文提出的算法可以找到问题的最优解，并在可行集凸包的1骨骼中找到从初始解到找到的最优解的路径。该路径的长度由可行解决方案的组成部分可以采用的各个不同值的总和限制，而不是问题的范围。特别地，在可行集是二进制矢量集的情况下，所构造路径的长度受变量数量的限制，而与目标函数无关。