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Schur Complement Trick for Positive Semi-definite Energies

Jacobson, Alec S.

The Schur complement trick appears sporadically in numerical optimization methods [Schur 1917; Cottle 1974]. The trick is especially useful for solving Lagrangian saddle point problems when minimizing quadratic energies subject to linear equality constraints [Gill et al. 1987]. Typically, to apply the trick, the energy's Hessian is assumed positive definite. I generalize this technique for positive semi-definite Hessians.

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Academic Units
Computer Science
Publisher
Department of Computer Science, Columbia University
Series
Columbia University Computer Science Technical Reports, CUCS-018-14
Published Here
June 17, 2014