Partially Augmented Lagrangian Method for Matrix Inequality Constraints

A partially augmented Lagrangian method for low order H-infinity controller synthesis using rational constraints, Report no. LiTH-ISY-R-3008

When designing robust controllers, H-in nity synthesis is a common tool to use. The controllers that result from these algorithms are typically of very high order, which complicates implementation. However, if a constraint on the maximum order of the controller is set, that is lower than the order of the (augmented) system, the problem becomes nonconvex and it is relatively hard to solve. These...

Local convergence of an augmented Lagrangian method for matrix inequality constrained programming

We consider nonlinear optimization programs with matrix inequality constraints, also known as nonlinear semidefinite programs. We prove local convergence for an augmented Lagrangian method which uses smooth spectral penalty functions. The sufficient second-order no-gap optimality condition and a suitable implicit function theorem are used to prove local linear convergence without the need to dr...

An Augmented Lagrangian Method for a Class of Lmi-constrained Problems in Robust Control Theory

We present a new approach to a class of non-convex LMI-constrained problem in robust control theory. The problems we consider may be recast as the minimization of a linear objective subject to linear matrix inequality (LMI) constraints in tandem with non-convex constraints related to rank conditions. We solve these problems using an extension of the augmented Lagrangian technique. The Lagrangia...

Updating Multipliers Corresponding to Inequality Constraints in an Augmented Lagrangian Multipliers Method

A NONLINEAR SDP ALGORITHM FOR STATIC OUTPUT FEEDBACK PROBLEMS IN COMPleib

We present an algorithm for the solution of static output feedback problems formulated as semidefinite programs with bilinear matrix inequality constraints and collected in the library COMPleib . The algorithm, based on the generalized augmented Lagrangian technique, is implemented in the publicly available general purpose software PENBMI. Numerical results demonstrate the behavior of the code....