A Successive Constraint Approach to Solving Parameter-Dependent Linear Matrix Inequalities
This work addresses the computational bottleneck of solving parameter-dependent LMIs for engineers and researchers in control and optimization, but the improvement is incremental.
The paper introduces a successive constraint approach with offline/online decomposition to efficiently solve large-scale parameter-dependent linear matrix inequalities for many parameter values, and extends it to semidefinite programming.
We present a successive constraint approach that makes it possible to cheaply solve large-scale linear matrix inequalities for a large number of parameter values. The efficiency of our method is made possible by an offline/online decomposition of the workload. Expensive computations are performed beforehand, in the offline stage, so that the problem can be solved very cheaply in the online stage. We also extend the method to approximate solutions to semidefinite programming problems.