The optimal decomposition method (ODM) for nonlinear problems

Jafarimoghaddam, Amin; Arnedo, Manuel Soler; Simorgh, Abolfazl

doi:10.1016/j.jocs.2022.101690

Cited by 2 publications

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References 28 publications

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“…This adjustment is known as Duan-Rach (D-R) ADM (see References 42 and 43). To track a frontier nonlinear decomposition solver, we refer to the optimal decomposition method (ODM) recently proposed by Jafarimoghaddam et al 44 . † Roughly speaking, HAM is distinguished by allowing other types of linear operators, or equivalently  −1 Ω , to appear.…”

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confidence: 99%

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Perturbed‐analytic direct transcription for optimal control (PADOC)

Jafarimoghaddam

Soler

2023

Optim Control Appl Methods

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The herein coined PADOC (perturbed-analytic direct transcription for optimal control) stands for a new transcription method for direct trajectory optimization. We construct PADOC on a novel segmented decomposition method that provides series solutions for nonlinear problems. To transcribe the infinite dimensional problem into a finite one, PADOC comes along with a new solution approach, namely, the herein coined average nonlinear programming (aNLP). The aNLP theorem suggests generating a staircase optimal solution (low resolution) and turning it into a distributed optimal solution (high resolution) by exploiting the Hamiltonian of the problem. The analytic architecture provides PADOC with an analytic connection of a truncated order between the discrete nodes of the solution. This renders stability, accuracy within an analytic resolution, robustness, and a cut-down in the number of the decision variables in the frame of NLP. We also prove that the multipliers associated with the Karush-Kuhn-Tucker optimality conditions in the frame of NLP (as transcribed by PADOC) correspond to a backward analytic solution for the costate equations. We finally show distinct features of PADOC through some examples.

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Section: Conflict Of Interestmentioning

confidence: 99%

“…This adjustment is known as Duan–Rach (D‐R) ADM (see References 42 and 43). To track a frontier nonlinear decomposition solver, we refer to the optimal decomposition method (ODM) recently proposed by Jafarimoghaddam et al 44 .…”

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confidence: 99%

Perturbed‐analytic direct transcription for optimal control (PADOC)

Jafarimoghaddam

Soler

2023

Optim Control Appl Methods

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An asymptotic matching approach to the approximate solution of the Blasius problem

Durante

2023

Physics of Fluids

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The Blasius equation dates back to the early twentieth century and describes the boundary layer caused by a uniform flow over a flat plate. Due to the asymptotic condition on the first derivative of the solution, the problem is not an initial value one. The non-linear nature of the equation has led many authors to exploit approximation strategies to obtain an estimate of the solution. Several papers deal with series expansions but the solutions are partly numerical and do not converge rapidly everywhere. In the present paper, a strategy is proposed to obtain an approximate solution of the Blasius problem in closed form, i.e. withoutthe use of series expansions. Motivated by the asymptotic behaviour of the second derivative, a parametric definition of the third derivative of the Blasius solution is introduced and successive integrations are performed. By imposing the expected asymptotic conditions, a final approximate solution is obtained. This latter has the notable advantage of possessing the same behaviour at 0 and at ∞ as the analytical solution up to the third derivative. It will also be shown how this result can be extended to the Falkner-Skan problem with non-zero pressure gradient and provide an accurate estimation of the thermal boundary layer over aflat plate under isothermal and adiabatic conditions.

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The optimal decomposition method (ODM) for nonlinear problems

Cited by 2 publications

References 28 publications

Perturbed‐analytic direct transcription for optimal control (PADOC)

Perturbed‐analytic direct transcription for optimal control (PADOC)

An asymptotic matching approach to the approximate solution of the Blasius problem

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