Products: QP Solver

ODYS QP solver

Fast and robust QP solver for embedded optimization


ODYS QP Solver is a fast and robust solver for Quadratic Programming (QP) problems. It is significantly optimized for problems arising in real-time embedded optimization and embedded MPC. It supports general inequality constraints, equality constraints, and bound constraints on the optimization variables.

Fast and Accurate

The solver is extremely fast and robust for QP problems of the typical size found in embedded optimization. In obtains high-accuracy optimal solutions in both single and double precision floating point arithmetic.
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Optimized for Model Predictive Control

The solver is very efficient to solve Model Predictive Control (MPC) problems. It exploits the special structure of the cost function and constraints to significantly reduce computation time and memory footprint.
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Certifiable execution time

Our proprietary certification package can compute in advance the exact worst-case execution time of the solver, for QP problems that depend linearly on parameters. This is very useful in embedded applications with hard real-time constraints to guarantee that task overruns never occur.
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Easy to deploy

The solver is efficiently coded in plain C, does not require external libraries and is compliant with MISRA-C 2012. The source code can be easily integrated into your target platform. We provide plug-and-play interfaces to Windows, Unix, Python, MATLAB/Simulink, R, and more.
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Get in touch with us to receive a free trial of the software or request a quote for the full version. We will be happy to discuss with you the needs of your application. If you use ODYS QP Solver in a scientific paper, please add a citation.

Performance

ODYS QP solver is designed to solve very efficiently small and medium scale convex quadratic programming problems of the form:

     {\footnotesize \begin{alignat*}{2} \underset{z}{\text{min.}}\quad &\dfrac{1}{2}z'Hz +h'z &\\ \text{s.t.}\quad & A_{in}z\le b_{in} &\text{(inequality constraints)} \\ & A_{eq}z= b_{eq} &\text{(equality constraints)}\\ & l_b \le z\le u_b &\text{(bound constraints)} \end{alignat} }

We have successfully applied the solver in many real-time optimization problems that require computing the solution in the milliseconds range and on limited computational resources. It is fast and has low memory occupancy. It provides accurate and robust results even when used in single precision arithmetic.

The tables on the right show the results obtained by running the solver on an Intel Core i7 2.5GHz, for dense QP problems of different sizes and with an average of 40% constraints active at the optimal solution.

Fast and robust QP solver

Fast and robust QP solver

Integration with Model Predictive Control

Solving QP problems efficiently is the key enabler for deploying real-time linear and nonlinear model predictive control in industrial production.

Although the basic version of ODYS QP solver software can already solve problems arising from MPC, we have developed a dedicated MPC version to further improve both the speed of execution and the memory occupancy of the optimization algorithm.

By exploiting the special structure of the cost function and constraints of a predictive control problem formulation, the MPC version of ODYS QP solver is twice as fast and take half the memory than the basic version, on typical embedded control problems.

The QP solver is part of ODYS’ proprietary C code for real-time implementation of embedded MPC controllers in industrial applications.

Certification of execution time

Quantifying with accuracy the worst-case execution time of the optimizer is typically necessary in industrial embedded systems, to meet real-time requirements and avoid oversizing the processor.

Most QP algorithms simply impose a maximum number of iterations to make sure that the problem is solved within the prescribed amount of time, without any guarantee on the quality of the computed solution. On the other hand, ODYS QP solver comes with a complexity analyzer that computes exactly the maximum number of iterations needed to reach the optimal solution, for a given set of problems that depend linearly on parameters, with no over-estimation!

This is helpful to select the appropriate computing hardware in the control design phase, to validate an existing design, and to identify possible situations where the problem is infeasible.

 

Fast and robust QP solver

Fast and robust QP solver

Cross-platform deployment

ODYS QP Solver is distributed as a shared library and supports all the main operating systems, in 32-bit and 64-bit architectures.

The software includes built-in interfaces and demos for MATLAB/Simulink, Python and C. Customers can readily integrate it in any framework that allows importing shared libraries.

The solver is coded in plain C, is compliant with MISRA-C 2012 requirements, and does not require any OS-dependent function or library. As such, the solver can be compiled on virtually any platform supporting floating point operations.

Please contact us if you are interested in acquiring a license and obtaining the source code for compiling the solver in your desired target platform.

 

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