Eigendecomposition of Q in Equally Constrained Quadratic Programming
This work addresses an incremental improvement in optimization methods for specific domains like finance and machine learning, with limited direct impact.
The paper tackles the problem of solving equally constrained quadratic programming (EQP) by diagonalizing the quadratic term matrix and establishing a linear mapping to project optimal solutions between the original and diagonalized formulations. The result is a generalizable method applicable to problems like portfolio allocation and LSSVM classification, though its practical utility remains unclear.
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.