For quadratic cone programs with strongly convex objectives, choosing the objective scaling factor as sqrt(sigma_min / 2) provably minimizes the KKT condition number, and packaging this with hypersphere and row-normalization steps yields a fast, factorization-free preconditioner.
Neuromorphic quadratic programming for efficient and scalable model predictive control
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abstract
Applications in robotics or other size-, weight- and power-constrained autonomous systems at the edge often require real-time and low-energy solutions to large optimization problems. Event-based and memory-integrated neuromorphic architectures promise to solve such optimization problems with superior energy efficiency and performance compared to conventional von Neumann architectures. Here, we present a method to solve convex continuous optimization problems with quadratic cost functions and linear constraints on Intel's scalable neuromorphic research chip Loihi 2. When applied to model predictive control (MPC) problems for the quadruped robotic platform ANYmal, this method achieves over two orders of magnitude reduction in combined energy-delay product compared to the state-of-the-art solver, OSQP, on (edge) CPUs and GPUs with solution times under ten milliseconds for various problem sizes. These results demonstrate the benefit of non-von-Neumann architectures for robotic control applications.
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Optimal Preconditioning for Online Quadratic Cone Programming
For quadratic cone programs with strongly convex objectives, choosing the objective scaling factor as sqrt(sigma_min / 2) provably minimizes the KKT condition number, and packaging this with hypersphere and row-normalization steps yields a fast, factorization-free preconditioner.