Development of highly accurate algorithms for semidefinite programming problems

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We mainly proposed an algorithm to remove ill-conditionedness in a given semidefinite programming problems (SDPs). In particular, we focus on ill-conditioned SDP, i.e., the SDP or its dual do not have any interior feasible solutions. Our results are: (1) We proposed a pre-processor for ill-conditioned SDP. It generates an equivalent and well-conditioned SDP with the original. Furthermore, we proposed a similar pre-processor for conic optimization problems, (2) We traced a reason why the resulting SDP from some applications are ill-conditioned, (3) We proposed an algorithm to generate well-conditioned SDP for polynomial optimization problems.