Formal Verification for Embedded Implementation of Convex Optimization Algorithms

Cohen, Raphael; Davy, Guillaume; Féron, Éric; Garoche, P.

doi:10.1016/j.ifacol.2017.08.1300

Cited by 5 publications

(6 citation statements)

References 18 publications

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“…Narkawicz and Muñoz [34] have devised a verified numeric algorithm to find bounds and global optima. Cohen et al [10,11] have developed a framework for verifying optimization algorithms using the ANSI/ISO C Specification Language (ACSL) [5].…”

Section: Related Workmentioning

confidence: 99%

Verified reductions for optimization

Bentkamp¹,

Fernández²,

Avigad³

2023

Preprint

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Numerical and symbolic methods for optimization are used extensively in engineering, industry, and finance. Various methods are used to reduce problems of interest to ones that are amenable to solution by these methods. We develop a framework for designing and applying such reductions, using the Lean programming language and interactive proof assistant. Formal verification makes the process more reliable, and the availability of an interactive framework and ambient mathematical library provides a robust environment for constructing the reductions and reasoning about them.

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Section: Related Workmentioning

confidence: 99%

Verified reductions for optimization

Bentkamp¹,

Fernández²,

Avigad³

2023

Preprint

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“…The iEHO algorithm is considered here at the expense of other swarm-based ones, due to its reduced number of tuning parameters and its proven effectiveness in the specific problem under study [28,29,53]. In addition, its simplicity contrasts the need for matrix calculations and other essential complex mathematical calculation in the deterministic context [69,70]. In order to get a better understanding and appreciation of the obtained results, the standard EHO is also implemented and evaluated for comparison.…”

Section: Swarm Optimizationmentioning

confidence: 99%

Development of a Test-Bench for Evaluating the Embedded Implementation of the Improved Elephant Herding Optimization Algorithm Applied to Energy-Based Acoustic Localization

et al. 2020

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The present work addresses the development of a test-bench for the embedded implementation, validity, and testing of the recently proposed Improved Elephant Herding Optimization (iEHO) algorithm, applied to the acoustic localization problem. The implemented methodology aims to corroborate the feasibility of applying iEHO in real-time applications on low complexity and low power devices, where three different electronic modules are used and tested. Swarm-based metaheuristic methods are usually examined by employing high-level languages on centralized computers, demonstrating their capability in finding global or good local solutions. This work considers iEHO implementation in C-language running on an embedded processor. Several random scenarios are generated, uploaded, and processed by the embedded processor to demonstrate the algorithm’s effectiveness and the test-bench usability, low complexity, and high reliability. On the one hand, the results obtained in our test-bench are concordant with the high-level implementations using MatLab® in terms of accuracy. On the other hand, concerning the processing time and as a breakthrough, the results obtained over the test-bench allow to demonstrate a high suitability of the embedded iEHO implementation for real-time applications due to its low latency.

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“…Research has also been made toward the verification of numerical optimization algorithms [11,12], yet it remains purely theoretical and no proof was obtained using formal verification tools. Contributions on formal verification of optimization algorithms have already been made [13], but this work focuses on a single optimization problem, where closed-loop behaviors are not being addressed, which does not meet the level of guarantees needed for receding horizon controllers. As well, the formal proof was not complete and no numerical analysis was presented.…”

Section: Introductionmentioning

confidence: 99%

“…• axiomatization of optimization problems and formalization of algorithm proof (Ellipsoid method) as code annotation • extraction of guarantees of convergence for sequential optimization problems, representing closed-loop management • modification of the original algorithm to account for floating-point errors • generation of C code implementations via credible autocoders of receding horizon controllers along with ANSI/ISO C Specification Language (ACSL) annotations The choice of ellipsoid method here seems unconventional as current state of art solvers typically use some variant of the interior-point method. However it has been shown in [13] that guaranteeing the numerical accuracy of second-order methods are very challenging. This paper is a first attempt at providing methods and tools to formally verify convex optimization code for solving online receding-horizon control problems.…”

Section: Introductionmentioning

confidence: 99%

Verification and Validation of Convex Optimization Algorithms for Model Predictive Control

Cohen

Féron

Garoche

2020

Journal of Aerospace Information Systems

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Advanced embedded algorithms are growing in complexity and they are an essential contributor to the growth of autonomy in many areas. However, the promise held by these algorithms cannot be kept without proper attention to the considerably stronger design constraints that arise when the applications of interest, such as aerospace systems, are safety-critical. Formal verification is the process of proving or disproving the "correctness" of an algorithm with respect to a certain mathematical description of it by means of a computer. This article discusses the formal verification of the Ellipsoid method, a convex optimization algorithm, and its code implementation as it applies to receding horizon control. Options for encoding code properties and their proofs are detailed. The applicability and limitations of those code properties and proofs are presented as well. Finally, floating-point errors are taken into account in a numerical analysis of the Ellipsoid algorithm. Modifications to the algorithm are presented which can be used to control its numerical stability.

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Formal Verification for Embedded Implementation of Convex Optimization Algorithms

Cited by 5 publications

References 18 publications

Verified reductions for optimization

Verified reductions for optimization

Development of a Test-Bench for Evaluating the Embedded Implementation of the Improved Elephant Herding Optimization Algorithm Applied to Energy-Based Acoustic Localization

Verification and Validation of Convex Optimization Algorithms for Model Predictive Control

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