An interior algorithm for nonlinear optimization that combines line search and trust region steps

Waltz, Richard A.; Morales, José Luís; Nocedal, Jorge; Orban, Dominique

doi:10.1007/s10107-004-0560-5

Cited by 903 publications

(476 citation statements)

References 28 publications

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“…First, we remark that in our analysis we use only small perpendicular and temporal baseline interferograms because the large baseline ones do not contribute with relevant information in equation (2), since the corresponding w k (·) values are very small (Zebker and Villasenor 1992). Second, we underline that the minimization of the non-linear functional in (2) can be performed by using one of the several non-linear optimization routines available in literature (Kirkpatrick et al 1983, Zhu et al 1997, Waltz et al 2006. In particular, in this work we use the solver developed by Zhu et al (1997), which implements a limited memory quasi-Newton approach that is particularly suitable to solve constrained/unconstrained large non-linear optimization problems, by guaranteeing stable results and high computational efficiency.…”

Section: Interferogram Noise-filtering Algorithmmentioning

confidence: 99%

A simple solution to mitigate noise effects in time-redundant sequences of small baseline multi-look DInSAR interferograms

Yang

Pepe

Manzo

et al. 2013

Remote Sensing Letters

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Letters, 2013 Vol. 4, No. 6, 609-618, http://dx.doi.org/10.1080/2150704X.2013 A simple solution to mitigate noise effects in time-redundant sequences of small baseline multi-look DInSAR interferograms We present a simple and effective filtering algorithm to mitigate noise effects in a time-redundant sequence of multi-look small baseline (SB) differential synthetic aperture radar (SAR) interferograms by exploiting the temporal relationships among the selected interferometric data pairs. The proposed method relies on the estimation of the (wrapped) filtered phase terms associated to each SAR acquisition; this result is achieved via a non-linear minimization procedure which is applied to the phase signal of conventional multi-look interferograms without any pixel selection process, and with no a-priori information on the statistics of the involved complex-valued SAR images. Following their estimation, the phase images are paired to reconstruct a new sequence of filtered SB differential interferograms, which are used to generate surface deformation products, such as deformation velocity maps and displacement time-series. The filtering algorithm effectiveness is demonstrated by analysing a set of SAR images acquired by the ENVISAT sensor from 2003 to 2010 over the city of Shanghai, China.

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Section: Interferogram Noise-filtering Algorithmmentioning

confidence: 99%

A simple solution to mitigate noise effects in time-redundant sequences of small baseline multi-look DInSAR interferograms

Yang

Pepe

Manzo

et al. 2013

Remote Sensing Letters

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“…The scale dependence of such a parameter is not ideal, but a bound similar to (3.5b) is used to ensure the boundedness of the penalty parameter π k (as we show in Lemma 4.7) if the rule (3.6) is enforced. Since such a method for setting the penalty parameter has proved to work well in practice [23], we employ this update rule in the algorithms in this paper and define β and (3.5b) as given. The constants (τ, σ, η) can generally be set to default values, or, in the case of σ, to promote consistency between Termination Tests I and II.…”

Section: 1mentioning

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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“…Loqo [33] implements a line search primal-dual algorithm that can be viewed as a direct extension of interior methods for linear and quadratic programming. The first release of Knitro [6] offered a trust region interior-point algorithm employing a conjugate gradient iteration in the step computation; the second release added a line search interior algorithm that is safeguarded by the trust region approach [38]. Barnlp [2] and Ipopt [36] implement line search interior-point approaches; Ipopt uses a filter globalization and includes a feasibility restoration phase.…”

Section: Introductionmentioning

confidence: 99%

Knitro: An Integrated Package for Nonlinear Optimization

Byrd

Nocedal

Waltz

2006

Nonconvex Optimization and Its Applications

754

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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An interior algorithm for nonlinear optimization that combines line search and trust region steps

Cited by 903 publications

References 28 publications

A simple solution to mitigate noise effects in time-redundant sequences of small baseline multi-look DInSAR interferograms

A simple solution to mitigate noise effects in time-redundant sequences of small baseline multi-look DInSAR interferograms

An Inexact SQP Method for Equality Constrained Optimization

Knitro: An Integrated Package for Nonlinear Optimization

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