抄録
Offer Organization: Japan Society for the Promotion of Science, System Name: Grants-in-Aid for Scientific Research, Category: Grant-in-Aid for Scientific Research (B), Fund Type: -, Overall Grant Amount: - (direct: 7200000, indirect: 2160000)
Interior-point algorithms for semidefinite programs and symmetric cone programs are analyzed in view of information geometry to show that the iteration complexity of primal-dual interior-point algorithms is approximately represented as a infomration geometric integral over central trajectory. Through extensive numerical experiments we demonstrated that the integral very accurately predict iteration-complexity of interior-point algorithms. One of the largest Gaussian graphical models in the world are successfully solved with super computer. Primal-dual interior-pont algorithms for large-scale Gaussian graphical models are developed. Regularization and facial reduction approaches for ill-conditioned semidefinite programs are developed.