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• W2024457515 abstract "Most current implementations of interior-point methods for semidefinite programming use a direct method to solve the Schur complement equation (SCE) $M Delta y=h$ in computing the search direction. When the number of constraints is large, the problem of having insufficient memory to store M can be avoided if an iterative method is used instead. Numerical experiments have shown that the conjugate residual (CR) method typically takes a huge number of steps to generate a high accuracy solution. On the other hand, it is difficult to incorporate traditional preconditioners into the SCE, except for block diagonal preconditioners. We decompose the SCE into a 2 × 2 block system by decomposing $Delta y$ (similarly for h) into two orthogonal components with one lying in a certain subspace that is determined from the structure of M. Numerical experiments on semidefinite programming problems arising from the Lovász $theta$-function of graphs and MAXCUT problems show that high accuracy solutions can be obtained with a moderate number of CR steps using the proposed equation." @default.
• W2024457515 created "2016-06-24" @default.
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• W2024457515 date "2002-01-01" @default.
• W2024457515 modified "2023-10-16" @default.
• W2024457515 title "Solving Some Large Scale Semidefinite Programs via the Conjugate Residual Method" @default.
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• W2024457515 doi "https://doi.org/10.1137/s1052623400376378" @default.
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