This study presents a novel algorithm for computing the convex hull of a point set in high-dimensional Euclidean space. The proposed method iteratively solves a sequence of dynamically updated quadratic programming (QP) problems for each point and exploits their solutions to establish theoretical guarantees for exact convex hull identification. For a dataset of \( n \) points in an \( m \)-dimensional space, the algorithm attains a dimension-independent worst-case time complexity of \( O(n^{p+2}) \), where \( p \) depends on the choice of QP solver (e.g., \( p = 4 \) corresponds to the worst-case bound using an interior-point method). The approach is particularly effective for large-scale, high-dimensional datasets, where existing exponential-time algorithms are computationally impractical.

翻译：本研究提出了一种计算高维欧几里得空间中点集凸包的新算法。该方法通过为每个点迭代求解一系列动态更新的二次规划问题，并利用其解为精确凸包识别建立理论保证。对于m维空间中的n个点数据集，该算法实现了与维度无关的最坏情况时间复杂度O(n^{p+2})，其中p取决于二次规划求解器的选择（例如，使用内点法时p=4对应最坏情况边界）。该方法特别适用于大规模高维数据集，在这些场景下现有的指数时间算法在计算上不切实际。