joint work with Masakazu Kojima, Kim-Chuan Toh
We exploit sparsity of the doubly nonnegative (DNN) relaxation and the completely positive (CPP) reformulation via the CPP and DNN matrix completion. The equivalence between the CPP and DNN relaxation is established under the assumption that the sparsity of the CPP relaxation is represented with block clique graphs with the maximal clique size at most 4. We also show that a block diagonal QOP with the maximal clique of size 3 over the standard simplex can be reduced to a QOP whose optimal value can be exactly computed by the DNN relaxation.
joint work with Bruno Figueira Lourenço, Masakazu Muramatsu
Recently, Lourenco et al. proposed an extension of Chubanov's projection and rescaling algorithm for symmetric cone programming. Muramatsu et al. also proposed an oracle-based projection and rescaling algorithm for semi-infinite programming. Both projection and rescaling algorithms can naturally deal with semidefinite programming. We implemented both algorithms in MATLAB and numerically compare them.
joint work with Mituhiro Fukuda, Sunyoung Kim, Takashi Nakagaki
In this talk, we discuss a spectral projected gradient (SPG) method designed for the dual problem of a log-determinant semidefinite problems (SDPs) with general linear constraints. The feasible region of the dual problem is an intersection of a box-constrained set and a linear matrix inequality. In contrast to a simple SPG that employs a single projection onto the intersection, the proposed method utilizes the structure of two projections for the two sets. Numerical results on randomly generated synthetic/deterministic data and gene expression data show the efficacy of the proposed method.