# On Generalizing Trace Minimization

@article{Liang2021OnGT, title={On Generalizing Trace Minimization}, author={Xin Liang and Li Wang and Lei-Hong Zhang and Ren-Cang Li}, journal={ArXiv}, year={2021}, volume={abs/2104.00257} }

Ky Fan’s trace minimization principle is extended along the line of the Brockett cost function tr(DXAX) in X on the Stiefel manifold, where D of an apt size is positive definite. Specifically, we investigate infX tr(DX AX) subject to XBX = Ik or Jk = diag(±1). We establish conditions under which the infimum is finite and when it is finite, analytic solutions are obtained in terms of the eigenvalues and eigenvectors of the matrix pencil A−λB, where B is possibly indefinite and singular, and D is…

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