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 (C), Fund Type: -, Overall Grant Amount: - (direct: 3500000, indirect: 1050000)
There are two major achievements in this project. The first one is to show that the upper bound of the iterations of Facial Reduction Algorithms (FRA) applied to a (nonlinear) cone containing polyhedral cones, depends only on that of the nonlinear part; in other words, we can safely ignore the polyhedral cones at least from the viewpoint of FRA. The other is to extend two of Chubanov's algorithms proposed for homogeneous LPs using projection and rescaling to symmetric cones and semi-infinite polyhedral cones, respectively. For these algorithms, we implemented them only for the semidefinite programming problem and conducted numerical experiments. The latter algorithm evaluates the number of iterations using the "volume" of the feasible region as the conditional number. Especially if if the condition number is zero, then FRA, the main theme of this project, should be applied to the conic programming problem.