Existence and Uniqueness of Search Directions in Interior-Point Algorithms for the SDP and the Monotone SDLCP

Various search directions used in interior-point algorithms for the semidefinite program (SDP) and the monotone semidefinite linear complementarity problem (SDLCP) are characterized by the intersection of a maximal monotone affine subspace and a maximal and strictly antitone affine subspace. This observation provides a unified geometric view over the existence of those search directions.

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