Semidefinite and Cone Programming: Theory, Implementation and Applications

摘要

This proposal addresses the development of the theory and implementation of algorithms for semidefinite programming (SDP) and also investigates the applications of SDP. The objectives of this research project consist of: 1) advancing the knowledge of the theory and implementation of second-order primal-dual methods for SDP; 2) developing primal-dual interior- point (IP) algorithms to solve more general classes of problems; 3) enhancing the variety, applicability, usefulness, and robustness of first-order nonlinear programming methods for SDP; 4) investigating the use of first-order methods for solving extremely large linear programs that are not efficiently solvable by the simplex method or IP methods; 5) developing SDP-based methods for solving combinatorial optimization problems; and 6) implementing each of these ideas to compare them with existing methods and also to provide software for the research community. This research will lead to new and improved algorithms and codes to find exact or approximate solutions to optimization problems arising in diverse applications in industry, finance, science, and engineering.