Eigendecomposition of Q in Equally Constrained Quadratic Programming
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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 <cit.>, but its current proof is much improved and generalized. To the author's knowledge, very few similar discussion appears in literature.
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