joint work with Akihiro Tanaka, Akiko Yoshise
Large and sparse polyhedral approximations of the semidefinite cone have been showed important for solving hard conic optimization problems. We propose new approximations that contain the diagonally dominant cone and are contained in the scaled diagonally dominant cone, by devising a simple expansion of the semidefinite bases. As their applications, we propose 1. methods for identifying elements in certain cones, 2. cutting plane methods for conic optimization and 3. a Lagrangian-DNN method for some quadratic optimization problems. Numerical results showed the efficiency of these methods.
joint work with Akiko Yoshise
We propose a new method for solving SDP problems based on primal dual interior point method and ADMM, called Centering ADMM (CADMM). CADMM is an ADMM but it has the feature of updating the variables toward the central path. We conduct numerical experiments with SDP relaxation problems of QAP and compare CADMM with ADMM. The results demonstrate that which of two methods is favorable depends on instances.
joint work with Makoto Yamashita, Tim J. Mullin
Our research is focused on an optimal contribution selection (OCS) problem in equal deployment, which is one of the optimization problems that aims to maximize the total benefit under a genetic diversity constraint. The constraint allows the OCS problem to be modeled as mixed-integer second-order cone programming (MI-SOCP). We proposed a cone decomposition method (CDM) that is based on a geometric cut in combination with a Lagrangian multiplier method. We also utilized the sparsity found in OCS, into a sparse linear approximation, that can strongly enhance the performance of CDM.