  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 of
the algorithm based on the real computation model proposed by Blum, Shub and
Smale (the BSS model) which is more suitable for floating point computation in
modern computers. The adoption of the BBS model makes our description and
analysis much simpler than the original one by Chubanov [5]. Then we
reformulate semidefinite programming (SDP) and second-order cone programming
(SOCP) into LSIP, and apply our algorithm to obtain new complexity results for
computing interior feasible solutions of homogeneous SDP and SOCP.
