Nonlinear programming algorithms using trust regions and augmented Lagrangians with nonmonotone penalty parameters

Gomes, Francisco A. M.; Maciel, María Cristina; Martínez, José Mário

doi:10.1007/s10107980014a

Cited by 46 publications

(55 citation statements)

References 19 publications

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“…Baseado em (Gomes et al, 1999), a restrição de região de confiança (2d)é aqui definida usando a norma infinita, ou seja, O subproblema verticalé definido como:…”

Section: A Técnica De Região De Confian-ca De Byrd E Omojokununclassified

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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“…Baseado em (Gomes et al, 1999), a restrição de região de confiança (2d)é aqui definida usando a norma infinita, ou seja, O subproblema verticalé definido como:…”

Section: A Técnica De Região De Confian-ca De Byrd E Omojokununclassified

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

Sousa

Torres

2010

Sba Controle & Automação

View full text Add to dashboard Cite

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“…Algorithms based on the sequential quadratic programming (SQP) approach are among the most effective methods for solving (1). Some interesting algorithms of this class are given, for example, in [3,4,10,21]. A complete coverage of such methods can be found in [6,20].…”

Section: Mixing Merit Function and Filter Ideasmentioning

confidence: 99%

“…The algorithm presented in this paper will inherit the structure of the merit function based SQP method proposed in [10], hereafter called the GMM algorithm.…”

Section: A Prototypical Sqp Algorithmmentioning

confidence: 99%

“…A trust region approach is used as the globalization strategy. All of the iterates are required to satisfy the bound constraints l ≤ x ≤ u, so the merit function chosen was the augmented Lagrangian, written here (and in [10]) in an unusual way as L(x, λ, θ) = θ f (x) + C(x) T …”

Section: A Prototypical Sqp Algorithmmentioning

confidence: 99%

“…As shown in [10], the adoption of a non-monotone strategy for the reduction of θ is very effective to avoid this premature step shortening. However, it also allows the algorithm to cycle between small and large penalty parameters, FRANCISCO A.M. GOMES 341 inducing some zigzagging in many cases.…”

Section: A Prototypical Sqp Algorithmmentioning

confidence: 99%

See 2 more Smart Citations

A sequential quadratic programming algorithm that combines merit function and filter ideas

Gomes¹

2007

Mat. apl. comput.

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Abstract.A sequential quadratic programming algorithm for solving nonlinear programming problems is presented. The new feature of the algorithm is related to the definition of the merit function. Instead of using one penalty parameter per iteration and increasing it as the algorithm progresses, we suggest that a new point is to be accepted if it stays sufficiently below the piecewise linear function defined by some previous iterates on the ( f, C 2 2 )-space. Therefore, the penalty parameter is allowed to decrease between successive iterations. Besides, one need not to decide how to update the penalty parameter. This approach resembles the filter method introduced by Fletcher and Leyffer [Math. Program., 91 (2001), pp. 239-269], but it is less tolerant since a merit function is still used. Numerical comparison with standard methods shows that this strategy is promising. 65K05, 90C55, 90C30, 90C26. Mathematical subject classification:

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An algorithm for the topology optimization of geometrically nonlinear structures

Gomes

Senne

2014

Numerical Meth Engineering

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SUMMARYMost papers on topology optimization consider that there is a linear relation between the strains and displacements of the structure, implicitly assuming that the displacements of the structure are small. However, when the external loads applied to the structure are large, the displacements also become large, so it is necessary to suppose that there is a nonlinear relation between strains and displacements. In this case, we say that the structure is geometrically nonlinear. In practice, this means that the linear system that needs to be solved each time the objective function of the problem is evaluated is replaced by an ill‐conditioned nonlinear system of equations. Moreover, the stiffness matrix and the derivatives of the problem also become harder to compute.The objective of this work is to solve topology optimization problems under large displacements through a new optimization algorithm, named sequential piecewise linear programming. This method relies on the solution of convex piecewise linear programming subproblems that include second order information about the objective function. To speed up the algorithm, these subproblems are converted into linear programming ones. The new algorithm is not only globally convergent to stationary points but our numerical experiments also show that it is efficient and robust. Copyright © 2014 John Wiley & Sons, Ltd.

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Nonlinear programming algorithms using trust regions and augmented Lagrangians with nonmonotone penalty parameters

Cited by 46 publications

References 19 publications

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

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

A sequential quadratic programming algorithm that combines merit function and filter ideas

An algorithm for the topology optimization of geometrically nonlinear structures

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