Trust Region Methods

Conn, Andrew R.; Gould, Nicholas I. M.; Toint, Philippe L.

doi:10.1137/1.9780898719857

Cited by 2,539 publications

(2,292 citation statements)

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“…The variation of the sparse grid allows us to use models of different fidelity in the optimization. We use the trust-region framework [2,21] to adjust the model fidelity, in our case the sparse-grid collocation points, to the progress of the optimization algorithm. We first describe the trust-region framework, including the recent retrospective trust-region (RTR) algorithm [8], and then we describe how we compute our models when the optimization problem is given by (2.3), (3.2).…”

Section: Choice Of Collocation Points: Generalized Sparse Gridsmentioning

confidence: 99%

“…We make the following assumptions for the RTR method. Similar assumptions are made for the classical trust-region (CTR) method [21]. Assumption 4.1.…”

Section: Choice Of Collocation Points: Generalized Sparse Gridsmentioning

confidence: 99%

“…For the discontinuous diffusion and Burgers examples we employ the CTR algorithm [21] and the RTR algorithm [8] to guide adaptivity. We compare the results of CTR and RTR with those of a Newton-CG algorithm applied to a fixed highfidelity stochastic collocation discretization of the optimization problem [38].…”

Section: Note That If There Existsmentioning

confidence: 99%

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A Trust-Region Algorithm with Adaptive Stochastic Collocation for PDE Optimization under Uncertainty

Kouri¹,

Heinkenschloss²,

Ridzal³

et al. 2013

SIAM J. Sci. Comput.

108

116

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Abstract. The numerical solution of optimization problems governed by partial differential equations (PDEs) with random coefficients is computationally challenging because of the large number of deterministic PDE solves required at each optimization iteration. This paper introduces an efficient algorithm for solving such problems based on a combination of adaptive sparse-grid collocation for the discretization of the PDE in the stochastic space and a trust-region framework for optimization and fidelity management of the stochastic discretization. The overall algorithm adapts the collocation points based on the progress of the optimization algorithm and the impact of the random variables on the solution of the optimization problem. It frequently uses few collocation points initially and increases the number of collocation points only as necessary, thereby keeping the number of deterministic PDE solves low while guaranteeing convergence. Currently an error indicator is used to estimate gradient errors due to adaptive stochastic collocation. The algorithm is applied to three examples, and the numerical results demonstrate a significant reduction in the total number of PDE solves required to obtain an optimal solution when compared with a Newton conjugate gradient algorithm applied to a fixed high-fidelity discretization of the optimization problem.

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Section: Choice Of Collocation Points: Generalized Sparse Gridsmentioning

confidence: 99%

“…We make the following assumptions for the RTR method. Similar assumptions are made for the classical trust-region (CTR) method [21]. Assumption 4.1.…”

Section: Choice Of Collocation Points: Generalized Sparse Gridsmentioning

confidence: 99%

See 1 more Smart Citation

A Trust-Region Algorithm with Adaptive Stochastic Collocation for PDE Optimization under Uncertainty

Kouri¹,

Heinkenschloss²,

Ridzal³

et al. 2013

SIAM J. Sci. Comput.

108

116

View full text Add to dashboard Cite

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“…One might take η 0 = 0 so that all steps that provide a descent in the objective function are considered regardless of how small the reduction is with respect to the model reduction. However, stronger theoretical convergence results are proven for the case η 0 > 0 [6]. In our experiments we have used the following values: η 0 = 10 −4 , η 1 = 0.05, η 2 = 0.9, λ 0 = 0.0625, λ 1 = 0.25 and λ 2 = 2.5.…”

Section: End Ifmentioning

confidence: 99%

Trust Region versus Line Search for Computing the Optical Flow

Kalmoun¹,

Garrido²

2013

Multiscale Model. Simul.

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Abstract. We consider the numerical treatment of the optical flow problem by evaluating the performance of the trust region method versus the line search method. To the best of our knowledge, the trust region method is studied here for the first time for variational optical flow computation. Four different optical flow models are used to test the performance of the proposed algorithm combining linear and nonlinear data terms with quadratic and TV regularization. We show that trust region often performs better than line search; especially in the presence of non-linearity and non-convexity in the model.

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“…Essa região fechadaé assim denominada porque dentro dela o modelo quadrá-tico pode ser confiado como uma boa aproximação para a função objetivo não-linear original. Os métodos de região de confiança diferem entre si na forma que modelam a função objetivo e tratam as restrições (Nocedal e Wright, 1999;Conn et al, 2000), principalmente as restrições de desigualdades. A técnica de Byrd e Omojokun estudada neste artigo pode ser vista como uma Programação Quadrática Sequencial (PQS) com uma região de confiança.…”

Section: Introductionunclassified

O Método de região de confiança de Byrd-Omojokun aplicado ao Fluxo de Potência Ótimo

Sousa

Torres

2010

Sba Controle & Automação

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Robust Optimal Power Flow by Byrd-Omojukun Trust Region MethodThis paper presents a globally convergent Optimal Power Flow (OPF) algorithm, i.e., an optimization algorithm capable of finding an OPF solution whenever a solution exists. As power systems become heavily loaded and operate close to security limits there is an increasing need for globally convergent OPF algorithms. The proposed algorithm uses the trust region technique of Byrd and Omojokun with the trust region constraint defined by the infinity norm. The subproblems generated in each trust region iteration are solved by primal-dual interior-point methods for quadratic programming. The focus of the proposed OPF algorithm is on the convergence robustness rather than on processing time. The simulations results with the IEEE test systems suggest the expected robustness of the approach.

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Trust Region Methods

Cited by 2,539 publications

References 0 publications

A Trust-Region Algorithm with Adaptive Stochastic Collocation for PDE Optimization under Uncertainty

A Trust-Region Algorithm with Adaptive Stochastic Collocation for PDE Optimization under Uncertainty

Trust Region versus Line Search for Computing the Optical Flow

O Método de região de confiança de Byrd-Omojokun aplicado ao Fluxo de Potência Ótimo

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