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We point out that Chubanov's oracle-based algorithm for linear programming[5] can be applied almost as it is to linear semi-infinite programming (LSIP).In this note, we describe the details and prove the polynomial complexity ofthe algorithm based on the real computation model proposed by Blum, Shub andSmale (the BSS model) which is more suitable for floating point computation inmodern computers. The adoption of the BBS model makes our description andanalysis much simpler than the original one by Chubanov [5]. Then wereformulate semidefinite programming (SDP) and second-order cone programming(SOCP) into LSIP, and apply our algorithm to obtain new complexity results forcomputing interior feasible solutions of homogeneous SDP and SOCP.

An oracle-based projection and rescaling algorithm for linear semi-infinite feasibility problems and its application to SDP and SOCP