On the global convergence of an SLP-filter algorithm that takes EQP steps

Chin, Choong Ming; Fletcher, R.

doi:10.1007/s10107-003-0378-6

Cited by 113 publications

(70 citation statements)

References 12 publications

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“…In addition, the incorporation of second derivative information in SQP methods has proved to be difficult. We use, instead a sequential linear-quadratic programming (SLQP) method [5,9,16] that computes a step in two stages, each of which scales up well with the number of variables. First, a linear program (LP) is solved to identify a working set.…”

Section: Active-set Sequential Linear-quadratic Programmingmentioning

confidence: 99%

“…Mosek [1] is a primal-dual interior-point method for convex optimization, and Pennon [25] follows an augmented Lagrangian approach. New active-set methods based on Sequential Linear-Quadratic Programming (SLQP) have recently been studied by Chin and Fletcher [9] and Byrd et al [5]. Unlike SQP methods, which combine the active-set identification and the step computation in one quadratic subproblem, SLQP methods decouple these tasks into two subproblems.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Knitro: An Integrated Package for Nonlinear Optimization

Byrd

Nocedal

Waltz

2006

Nonconvex Optimization and Its Applications

758

518

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This paper describes Knitro 5.0, a C-package for nonlinear optimization that combines complementary approaches to nonlinear optimization to achieve robust performance over a wide range of application requirements. The package is designed for solving large-scale, smooth nonlinear programming problems, and it is also effective for the following special cases: unconstrained optimization, nonlinear systems of equations, least squares, and linear and quadratic programming. Various algorithmic options are available, including two interior methods and an active-set method. The package provides crossover techniques between algorithmic options as well as automatic selection of options and settings.

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Section: Active-set Sequential Linear-quadratic Programmingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Knitro: An Integrated Package for Nonlinear Optimization

Byrd

Nocedal

Waltz

2006

Nonconvex Optimization and Its Applications

758

518

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show abstract

“…This approach was promptly followed by many authors, mainly in conjunction with SLP (sequential linear programming), SQP and interior-point type methods (see, for instance, [1,5,6,7,9,11,12,15,16,17,22,23,24,25]). …”

Section: The Filter Methodsmentioning

confidence: 99%

“…In this case, s c is only accepted if A opt red /P opt red > γ g is satisfied. Most filter algorithms, such as those presented in [5,7,9,16,17,22,23] include similar tests.…”

Section: Mixing Merit Function and Filter Ideasmentioning

confidence: 99%

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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“…To avoid using a penalty function, Fletcher and Leyffer [10] proposed filter techniques that allow a step to be accepted if it sufficiently reduces either the objective function or the constraint violation. For more theoretical and algorithmic details on filter methods, see, e.g., [4,9,11,14,24,25,26,27,28].…”

Section: Introductionmentioning

confidence: 99%

A new double trust regions SQP method without a penalty function or a filter

Zhu¹,

Pu²

2012

Comput. Appl. Math.

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Abstract.A new trust-region SQP method for equality constrained optimization is considered.This method avoids using a penalty function or a filter, and yet can be globally convergent to first-order critical points under some reasonable assumptions. Each SQP step is composed of a normal step and a tangential step for which different trust regions are applied in the spirit of Gould and Toint [Math. Program., 122 (2010), pp. 155-196]. Numerical results demonstrate that this new approach is potentially useful.Mathematical subject classification: 65K05, 90C30, 90C55.

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On the global convergence of an SLP-filter algorithm that takes EQP steps

Cited by 113 publications

References 12 publications

Knitro: An Integrated Package for Nonlinear Optimization

Knitro: An Integrated Package for Nonlinear Optimization

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

A new double trust regions SQP method without a penalty function or a filter

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