Exploiting Block Structures of KKT Matrices for Efficient Solution of Convex Optimization Problems

Abstract

Convex optimization solvers are widely used in the embedded systems that require sophisticated optimization algorithms including model predictive control (MPC). In this paper, we aim to reduce the online solve time of such convex optimization solvers so as to reduce the total runtime of the algorithm and make it suitable for real-time convex optimization. We exploit the property of the Karush–Kuhn–Tucker (KKT) matrix involved in the solution of the problem that only some parts of the matrix change during the solution iterations of the algorithm. Our results show that the proposed method can effectively reduce the runtime of the solvers.

Keywords

• Convex optimization
• linear solver
• Karush–Kuhn–Tucker (KKT)
• embedded systems