Successive Linearization Methods for Nonlinear Semidefinite Programs
Computational Optimization and Applications
Local convergence of an augmented Lagrangian method for matrix inequality constrained programming
Optimization Methods & Software
A primal-dual interior point method for nonlinear optimization over second-order cones
Optimization Methods & Software
A review of robust optimal design and its application in dynamics
Computers and Structures
A successive SDP-NSDP approach to a robust optimization problem in finance
Computational Optimization and Applications
A Newton-like method for solving rank constrained linear matrix inequalities
Automatica (Journal of IFAC)
On the convergence of augmented Lagrangian methods for nonlinear semidefinite programming
Journal of Global Optimization
A homotopy method for nonlinear semidefinite programming
Computational Optimization and Applications
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This paper discusses nonlinear optimization techniques in robust control synthesis, with special emphasis on design problems which may be cast as minimizing a linear objective function under linear matrix inequality (LMI) constraints in tandem with nonlinear matrix equality constraints. The latter type of constraints renders the design numerically and algorithmically difficult. We solve the optimization problem via sequential semidefinite programming (SSDP), a technique which expands on sequential quadratic programming (SQP) known in nonlinear optimization. Global and fast local convergence properties of SSDP are similar to those of SQP, and SSDP is conveniently implemented with available semidefinite programming (SDP) solvers. Using two test examples, we compare SSDP to the augmented Lagrangian method, another classical scheme in nonlinear optimization, and to an approach using concave optimization.