Techniques for Gradient-Based Bilevel Optimization with Non-smooth Lower Level Problems

Ochs, Peter; Ranftl, René; Brox, Thomas; Pock, Thomas

doi:10.1007/s10851-016-0663-7

Cited by 33 publications

(22 citation statements)

References 32 publications

(53 reference statements)

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“…Our approach is based on unrolling an iterative optimization algorithm that solves the lower-level problem together with backpropagation to derive the necessary gradients for the higher-level problem. Similar formulations have been successfully used in the context of image processing and machine learning [7], [25], [26].…”

Section: A Related Workmentioning

confidence: 99%

Trajectory Optimization With Implicit Hard Contacts

Carius

Ranftl

Koltun

et al. 2018

IEEE Robot. Autom. Lett.

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Section: A Related Workmentioning

confidence: 99%

Trajectory Optimization With Implicit Hard Contacts

Carius

Ranftl

Koltun

et al. 2018

IEEE Robot. Autom. Lett.

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“…This sequence converges to ϑ. Denotes by (v k , u k ) the solution of S(γ k ). Form the compactness of U ad we can extract a subsequence of v k (58)…”

Section: Differentiability Of the Functionmentioning

confidence: 99%

“…The discrete version of different operators appearing in the problem (65) are given in [1]. The learning parameter problem is solved via the classical projected gradient algorithm 2 [37,48,58].…”

Section: 2mentioning

confidence: 99%

A non-convex denoising model for impulse and Gaussian noise mixture removing using bi-level parameter identification

Afraites

Hadri

Laghrib

et al. 2022

IPI

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<p style='text-indent:20px;'>We propose a new variational framework to remove a mixture of Gaussian and impulse noise from images. This framework is based on a non-convex PDE-constrained with a fractional-order operator. The non-convex norm is applied to the impulse component controlled by a weighted parameter <inline-formula><tex-math id="M1">\begin{document}$ \gamma $\end{document}</tex-math></inline-formula>, which depends on the level of the impulse noise and image feature. Furthermore, the fractional operator is used to preserve image texture and edges. In a first part, we study the theoretical properties of the proposed PDE-constrained, and we show some well-posdnees results. In a second part, after having demonstrated how to numerically find a minimizer, a proximal linearized algorithm combined with a Primal-Dual approach is introduced. Moreover, a bi-level optimization framework with a projected gradient algorithm is proposed in order to automatically select the parameter <inline-formula><tex-math id="M2">\begin{document}$ \gamma $\end{document}</tex-math></inline-formula>. Denoising tests confirm that the non-convex term and learned parameter <inline-formula><tex-math id="M3">\begin{document}$ \gamma $\end{document}</tex-math></inline-formula> lead in general to an improved reconstruction when compared to results of convex norm and other competitive denoising methods. Finally, we show extensive denoising experiments on various images and noise intensities and we report conventional numerical results which confirm the validity of the non-convex PDE-constrained, its analysis and also the proposed bi-level optimization with learning data.</p>

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“…It is undeniable that the advantages of the last approach outweigh its drawbacks. The majority of the first optimization algorithms employed to solve engineering problems used gradient descent [1]. This means that they used to calculate the derivation of the problem to find an optimal solution starting from an initial design.…”

Section: Accepted Manuscriptmentioning

confidence: 99%

Optimization of problems with multiple objectives using the multi-verse optimization algorithm

Mirjalili

Jangir²,

Mirjalili

et al. 2017

Knowledge-Based Systems

245

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This work proposes the multi-objective version of the recently proposed Multi-Verse Optimizer (MVO) called Multi-Objective Multi-Verse Optimizer (MOMVO). The same concepts of MVO are used for converging towards the best solutions in a multi-objective search space. For maintaining and improving the coverage of Pareto optimal solutions obtained, however, an archive with an updating mechanism is employed. To test the performance of MOMVO, 80 case studies are employed including 49 unconstrained multi-objective test functions, 10 constrained multi-objective test functions, and 21 engineering design multi-objective problems. The results are compared quantitatively and qualitatively with other algorithms using a variety of performance indicators, which show the merits of this new MOMVO algorithm in solving a wide range of problems with different characteristics.

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Techniques for Gradient-Based Bilevel Optimization with Non-smooth Lower Level Problems

Cited by 33 publications

References 32 publications

Trajectory Optimization With Implicit Hard Contacts

Trajectory Optimization With Implicit Hard Contacts

A non-convex denoising model for impulse and Gaussian noise mixture removing using bi-level parameter identification

Optimization of problems with multiple objectives using the multi-verse optimization algorithm

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