Validation of Convex Optimization Algorithms and Credible Implementation for Model Predictive Control

Féron, Éric; Cohen, Raphael; Davy, Guillaume; Garoche, Pierre-Löıc

doi:10.2514/6.2017-0562

Cited by 2 publications

(2 citation statements)

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“…Linear programming does not allow to avoid the previous discussion about binary issues. On one hand, [11,8] manage to apply formal verification to the ellipsoid algorithm [15] with simple floating point representation using prior on the inputs. This result is important to advances on the application of a linear program solver on a critical task.…”

Section: Binary Consideration In Linear Programmingmentioning

confidence: 99%

“…Another one is to rely on standard routines and/or with the simplest possible algorithm. This explains why there is still research on old algorithm like the ellipsoid method [11,8]: even if it is the worst polynomial time algorithm for linear programming, it has some good features like the fact that it does not require matrix inversion. This also explains why, neither [20] nor [23] are fully satisfying as they require either custom routines or custom data-structure.…”

Section: Contribution: Dealing With Binary Issue With Standard Routinesmentioning

confidence: 99%

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A New Algorithm for Linear Programming in Critical Systems

Chan-Hon-Tong

2022

SN COMPUT. SCI.

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In critical systems (e.g. for core airplane functions), codes should both never fail, in particular they should be robust to numerical instabilities, and, they should reuse certified routines.Yet, the combination of this two constraints is often an issue. For example, the interior-point algorithms for linear programming have higher complexity than expected when requiring simultaneously numerical robustness and no custom routines.Instead, this paper presents a new algorithm, which has good time complexity even with a naive implementation. ForewordThis paper is an extended version of conference paper [5]. The main difference with [5] is that the proof is significantly simplified: there is no need to have a distinct part for each of the two so-called phases of the Newton descent anymore. Also, this paper describes, more precisely than [5], the interest of the new method to deal with critical systems regarding the state-of-the-art methods. NotationsThis paper takes advantage of standard matrix notation. In particular, if u, v are 2 vectors i.e. u, v ∈ R N u T v is the scalar product of the two vectors, because those vectors are seen like matrices in R N ×1 , thus, u T is a matrix in R 1×N , and thus, the matrix product uAlso, the scalar product of a vector u with itself (i.e. u T u) will be written ||u|| 2 2 in this paper using standard notation for the L 2 norm.

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Section: Binary Consideration In Linear Programmingmentioning

confidence: 99%