OpEn: Code Generation for Embedded Nonconvex Optimization (2003.00292v1)

Abstract: We present Optimization Engine (OpEn): an open-source code generation tool for real-time embedded nonconvex optimization, which implements a novel numerical method. OpEn combines the proximal averaged Newton-type method for optimal control (PANOC) with the penalty and augmented Lagrangian methods to compute approximate stationary points of nonconvex problems. The proposed method involves very simple algebraic operations such as vector products, has a low memory footprint and exhibits very good convergence properties that allow the solution of nonconvex problems on embedded devices. OpEn's core solver is written is Rust - a modern, high-performance, memory-safe and thread-safe systems programming language - while users can call it from Python, MATLAB, C, C++ or over a TCP socket.

OpEn: Code Generation for Embedded Nonconvex Optimization

The document introduces Optimization Engine (OpEn), a code generation tool specifically designed for real-time embedded nonconvex optimization tasks. The primary feature of OpEn is its implementation of a novel numerical method combining the Proximal Averaged Newton-type method for Optimal Control (PANOC) and penalty and augmented Lagrangian methods. The core solver is developed in Rust, known for its high performance and safety, and is accessible from various interfaces such as Python, MATLAB, and C.

Technical Details

OpEn is intended to address the computational challenges in embedded systems, characterized by limited resources and stringent runtime requirements. The tool allows users to solve nonconvex optimization problems by generating efficient code that can run on embedded devices with minimal overhead. The numerical method integrated within OpEn leverages PANOC, which has proven superior convergence properties compared to traditional methods such as Sequential Convex Programming (SCP) and Interior Point (IP) methods. PANOC employs simple algebraic operations, ensuring low memory usage, and is ideal for computing approximate stationary points of nonconvex problems efficiently.

Key Features

1. Code Generation: OpEn facilitates generation of embedded code for various system architectures, enabling integration with projects requiring real-time optimization solutions.
2. Convergence Efficiency: By using PANOC, OpEn achieves fast convergence rates suitable for real-time applications. This positions OpEn as a competitive option against prevalent nonconvex solvers.
3. Augmented Lagrangian Method: The innovative design considers constraints directly by applying penalty methods. This approach is particularly beneficial for embedded systems where computational capacity is restrictive.
4. Multi-Language Support: The solver core in Rust is interfaced with Python, MATLAB, and C/C++, providing versatility to incorporate OpEn in different technological environments.

Simulation Results

The paper provides simulation results illustrating the applicability of OpEn in two scenarios: obstacle avoidance and constrained nonlinear estimation. In the obstacle avoidance problem, OpEn outperformed other solvers like IPOPT and SLSQP in terms of execution speed, enabling efficient navigation of an autonomous ground vehicle. The constrained estimation for Lorenz's system substantiates OpEn’s computational efficiency with lower runtime compared to IPOPT for similar problem sizes. The ability to handle nonconvex problems rapidly on resource-constrained hardware exemplifies OpEn's potential for practical use in real-world applications.

Implications and Future Work

OpEn represents a significant step in the field of embedded nonconvex optimization, pushing the boundaries of what can be achieved on devices with limited computational resources. The integration of OpEn in edge computing and distributed systems highlights its capability to support advanced intelligent applications. Future research aims to refine convergence properties, especially for problems with complex constraint types. The ongoing development and refinement are expected to enhance its applicability to even broader contexts, following advancements in processor technologies and optimization algorithms.

In summary, OpEn provides a robust solution for those seeking to implement efficient nonconvex optimization strategies within embedded systems. It combines modern programming practices with cutting-edge numerical methods, enabling developers to harness its power across various domains where real-time computation is critical.