# A Successive Constraint Approach to Solving Parameter-Dependent Linear Matrix Inequalities

## TL;DR

The paper introduces a successive constraint method that efficiently solves large-scale parameter-dependent linear matrix inequalities by leveraging offline/online decomposition, enabling rapid solutions across many parameter values.

## Contribution

It presents a novel approach combining offline/online decomposition to efficiently solve parameter-dependent LMIs and extends it to semidefinite programming approximations.

## Key findings

- Significant reduction in online computation time.
- Effective handling of large-scale problems.
- Extension to semidefinite programming.

## Abstract

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.