A semidefinite program (SDP) is a special kind of convex optimization problem. It has a linear objective function with constraints on the eigenvalues of a linear matrix-valued function of the optimization variable. Many classical problems may be written as a SDP, including linear programs and convex quadratic programs. Engineering problems, such as synthesis of estimation and control algorithms, structural analysis and design, circuit design, model validation, and parameter estimation, can be reformulated as SDPs. The wide applicability of SDPs, and the availability of algorithms to solve them, suggests that semidefinite programming could become a viable tool for solving real-world problems.
In this talk we discuss
These points will be illustrated with three applications: attitude control in the Hubble Space Telescope, mistuning analysis in compressor rotors, and active structural control of an experimental building model.