Nonlinear programming without a penalty function

Fletcher, R.; Leyffer, Sven

doi:10.1007/s101070100244

Cited by 707 publications

(583 citation statements)

References 15 publications

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“…In this paper, we depict the general framework of a new SQP algorithm that combines ideas from both merit functions and the filter introduced by Fletcher and Leyffer in [8]. The use of several penalty parameters defined automatically by the previous iterates avoids the premature reduction of θ as well as the zigzagging that can occur when a non-monotone strategy is used to update this parameter.…”

Section: Discussionmentioning

confidence: 99%

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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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Section: Discussionmentioning

confidence: 99%

“…To overcome some of the difficulties inherent to merit functions, Fletcher and Leyffer [8] introduced the idea of using a filter. Instead of combining infeasibility and optimality in one single function, the filter method borrows the idea of nondominance from multi-criteria optimization theory.…”

Section: The Filter Methodsmentioning

confidence: 99%

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

Gomes¹

2007

Mat. apl. comput.

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“…Filter methods were first introduced by Fletcher and Leyffer [12] as a way to globalize sequential linear programming (SLP) and sequential quadratic programming (SQP) without using a penalty function. The Audet-Dennis GPS filter approach avoids the pitfalls of penalty parameters, but its convergence to standard first-order stationary points is not guaranteed [5] due to GPS limitations.…”

Section: Mesh Adaptive Direct Search (Mads)mentioning

confidence: 99%

“…Secondly, to be consistent with [11,12], only infeasible points are included in the filter, and feasible points are tracked separately. Using these two restrictions, we include the following terminology [3]: Definition 3.3 A point x is said to be filtered by a filter F if any of the following properties hold:…”

Section: Filtersmentioning

confidence: 99%

Characteristic Shape Sequences for Measures on Images

Pinge¹,

Abramson²,

Asaki³

et al. 2006

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Researchers in many fields often need to quantify the similarity between images using metrics that measure qualities of interest in a robust quantitative manner. We present here the concept of image dimension reduction through characteristic shape sequences. We formulate the problem as a nonlinear optimization program and demonstrate the solution on a test problem of extracting maximal area ellipses from twodimensional image data. To solve the problem numerically, we augment the class of mesh adaptive direct search (MADS) algorithms with a filter, so as to allow infeasible starting points and to achieve better local solutions. Results here show that the MADS filter algorithm is successful in the test problem of finding good characteristic ellipse solutions from simple but noisy images.

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“…The high level algorithm is suggested by Gonzaga et al [7] but not yet implemented -the internal algorithms are not proposed. The filter, a new concept introduced by Fletcher and Leyffer [3], replaces the merit function avoiding the penalty parameter estimation and the difficulties related to the nondifferentiability. In the IR approach two independent phases are performed in each iteration -the feasibility and the optimality phases.…”

mentioning

confidence: 99%

A filter inexact-restoration method for nonlinear programming

Silva

Monteiro

2008

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A new iterative algorithm based on the inexact-restoration (IR) approach combined with the filter strategy to solve nonlinear constrained optimization problems is presented. The high level algorithm is suggested by Gonzaga et al. [7] but not yet implemented -the internal algorithms are not proposed. The filter, a new concept introduced by Fletcher and Leyffer [3], replaces the merit function avoiding the penalty parameter estimation and the difficulties related to the nondifferentiability. In the IR approach two independent phases are performed in each iteration -the feasibility and the optimality phases. The line search filter is combined with the first one phase to generate a "more feasible" point and then it is used in the optimality phase to reach an "optimal" point.Numerical experiences with a collection of AMPL problems and a performance comparison with IPOPT are provided.

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Nonlinear programming without a penalty function

Cited by 707 publications

References 15 publications

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

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

Characteristic Shape Sequences for Measures on Images

A filter inexact-restoration method for nonlinear programming

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