Global Convergence of a Trust-Region SQP-Filter Algorithm for General Nonlinear Programming

Fletcher, R.; Gould, Nicholas I. M.; Leyffer, Sven; Toint, Philippe L.; Wächter, Andreas

doi:10.1137/s1052623499357258

Cited by 242 publications

(204 citation statements)

References 20 publications

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“…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%

“…The convex piecewise linear function that connects the points in F is defined by where γ s is a small positive constant, such as 10 −4 . This new function, illustrated in Figure 2, is formed by p + 1 line segments that can be viewed as merit functions in the form (7). The i-th of these functions is defined by the penalty parameter…”

Section: Mixing Merit Function and Filter Ideasmentioning

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%

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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: The Filter Methodsmentioning

confidence: 99%

Section: Mixing Merit Function and Filter Ideasmentioning

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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“…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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“…Assumption A3 is a standard one for similar algorithms (see [6,8,14,17,18,19]). It ensures that the algorithm produces a limit point.…”

Section: A2mentioning

confidence: 99%

Generalized pattern searches with derivative information

Abramson¹,

Audet

Dennis

2003

Math. Program., Ser. B

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Abstract.A common question asked by users of direct search algorithms is how to use derivative information at iterates where it is available. This paper addresses that question with respect to Generalized Pattern Search (GPS) methods for unconstrained and linearly constrained optimization. Specifically this paper concentrates on the GPS POLL step. Polling is done to certify the need to refine the current mesh, and it requires O(n) function evaluations in the worst case. We show that the use of derivative information significantly reduces the maximum number of function evaluations necessary for POLL steps, even to a worst case of a single function evaluation with certain algorithmic choices given here. Furthermore, we show that rather rough approximations to the gradient are sufficient to reduce the POLL step to a single function evaluation. We prove that using these less expensive POLL steps does not weaken the known convergence properties of the method, all of which depend only on the POLL step.

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Global Convergence of a Trust-Region SQP-Filter Algorithm for General Nonlinear Programming

Cited by 242 publications

References 20 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

Generalized pattern searches with derivative information

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