论文标题
Q在同样受约束的二次编程中的特征分类
Eigendecomposition of Q in Equally Constrained Quadratic Programming
论文作者
论文摘要
在一种类型的线性约束二次编程（EQP）中，将特征值分解应用于二次项矩阵（EQP）时，存在一个线性映射到新的EQP公式之间的项目最佳解决方案，其中$ q $在$ q $中是$ q $，$ q $是对角线化的，而原始格式则存在。尽管这样的映射需要特定类型的平等约束，但它可以推广到某些实际问题，例如用于投资组合分配的有效边界和最小二平方支持矢量机（LSSSVM）的分类。既定的映射可能对于探索子空间中的最佳解决方案可能是有用的，但对作者来说并不十分清楚。这项工作的灵感来自于在\ cite {tan}早期讨论的无约束配方的类似工作中的启发，但其当前证明得到了很大的改进和广泛化。据作者所知，文献中很少出现类似的讨论。
When applying eigenvalue decomposition on the quadratic term matrix in a type of linear equally constrained quadratic programming (EQP), there exists a linear mapping to project optimal solutions between the new EQP formulation where $Q$ is diagonalized and the original formulation. Although such a mapping requires a particular type of equality constraints, it is generalizable to some real problems such as efficient frontier for portfolio allocation and classification of Least Square Support Vector Machines (LSSVM). The established mapping could be potentially useful to explore optimal solutions in subspace, but it is not very clear to the author. This work was inspired by similar work proved on unconstrained formulation discussed earlier in \cite{Tan}, but its current proof is much improved and generalized. To the author's knowledge, very few similar discussion appears in literature.
