On the Implementation of an Algorithm for Large-Scale Equality Constrained Optimization

Lalee, Marucha; Nocedal, Jorge; Plantenga, Todd

doi:10.1137/s1052623493262993

Cited by 118 publications

(78 citation statements)

References 35 publications

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“…We note that a condition similar to (5.14) has been used for the merit function in a variety of trust region methods [8,14,16,29,34] that compute steps d without reference to a penalty function. Condition (5.14) has some resemblance to a condition proposed by Yuan [42] for adjusting the penalty parameter in an exact penalty method.…”

Section: Updating Guidelinesmentioning

confidence: 99%

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Steering exact penalty methods for nonlinear programming

Byrd

Nocedal

Waltz

2008

Optimization Methods and Software

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This paper reviews, extends and analyzes a new class of penalty methods for nonlinear optimization. These methods adjust the penalty parameter dynamically; by controlling the degree of linear feasibility achieved at every iteration, they promote balanced progress toward optimality and feasibility. In contrast with classical approaches, the choice of the penalty parameter ceases to be a heuristic and is determined, instead, by a subproblem with clearly defined objectives. The new penalty update strategy is presented in the context of sequential quadratic programming (SQP) and sequential linear-quadratic programming (SLQP) methods that use trust regions to promote convergence. The paper concludes with a discussion of penalty parameters for merit functions used in line search methods.

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Section: Updating Guidelinesmentioning

confidence: 99%

“…Several trust region algorithms [8,14,16,29,34] select the penalty parameter ν + at every iteration so that a condition like (7.22) is satisfied. (Some of these methods omit the factor ν from the right side of (7.22).…”

Section: Penalty Parameters In Merit Functionsmentioning

confidence: 99%

Steering exact penalty methods for nonlinear programming

Byrd

Nocedal

Waltz

2008

Optimization Methods and Software

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“…Jäger and Sachs [14] describe an inexact reduced SQP method in Hilbert space. Lalee, Nocedal, and Plantenga [16], Byrd, Hribar, and Nocedal [5], and Heinkenschloss and Vicente [13] propose composite step trust region approaches where the step is computed as an approximate solution to an SQP subproblem. Similarly, Walther [22] provides a composite step method that allows incomplete constraint Jacobian information.…”

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confidence: 99%

An Inexact SQP Method for Equality Constrained Optimization

Byrd¹,

Curtis²,

Nocedal³

2008

SIAM J. Optim.

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Abstract. We present an algorithm for large-scale equality constrained optimization. The method is based on a characterization of inexact sequential quadratic programming (SQP) steps that can ensure global convergence. Inexact SQP methods are needed for large-scale applications for which the iteration matrix cannot be explicitly formed or factored and the arising linear systems must be solved using iterative linear algebra techniques. We address how to determine when a given inexact step makes sufficient progress toward a solution of the nonlinear program, as measured by an exact penalty function. The method is globalized by a line search. An analysis of the global convergence properties of the algorithm and numerical results are presented.

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“…Em seguida, o valor tentativaé melhorado conforme o seguinte algoritmo proposto em (Lalee et al, 1998):…”

Section: Função Méritounclassified

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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On the Implementation of an Algorithm for Large-Scale Equality Constrained Optimization

Cited by 118 publications

References 35 publications

Steering exact penalty methods for nonlinear programming

Steering exact penalty methods for nonlinear programming

An Inexact SQP Method for Equality Constrained Optimization

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

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