A modification of Powell's dogleg method for solving systems of nonlinear equations

Chen, Hern-Shann; Stadtherr, Mark A.

doi:10.1016/0098-1354(81)85003-x

Cited by 63 publications

(34 citation statements)

References 6 publications

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“…The nonlinear set of equations is solved using NEQLU Ž . Chen and Stadtherr, 1981 . To facilitate and speed up the solving process, the algorithm considers only the units affected by the move, rather than the entire network.…”

Section: E©aluation and Assessmentmentioning

confidence: 95%

Scoping and screening complex reaction networks using stochastic optimization

Marcoulaki

Kokossis

1999

AIChE Journal

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Section: E©aluation and Assessmentmentioning

confidence: 95%

Scoping and screening complex reaction networks using stochastic optimization

Marcoulaki

Kokossis

1999

AIChE Journal

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“…To improve convergence in these circumstances, various methods have been used. These include trust-region techniques such as Powell's dogleg method (Powell, 1970;Chen and Stadtherr, 1981), homotopy-based methods (e.g., Wayburn and Seader, 1987;Kuno and Seader, 1988), and techniques based on iterative mathematical programming, as reviewed recently by Bullard and Biegler (1991).…”

Section: Introductionmentioning

confidence: 99%

Robust process simulation using interval methods

Schnepper

Stadtherr

1996

Computers & Chemical Engineering

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Ideally, for the needs of robust process simulation, one would like a nonlinear equation solving technique that can find any and all roots to a problem, and do so with mathematical certainty. In general, currently used techniques do not provide such rigorous guarantees. One approach to providing such assurances can be found in the use of interval analysis, in particular the use of interval Newton methods combined with generalized bisection. However, these methods have generally been regarded as extremely inefficient. Motivated by recent progress in interval analysis, as well as continuing advances in computer speed and the availability of parallel computing, we consider here the feasibility of using an interval Newton/generalized bisection algorithm on process simulation problems. An algorithm designed for parallel computing on an MIMD machine is described, and results of tests on several problems are reported. Experiments indicate that the interval Newton/generalized bisection method works quite well on relatively small problems, providing a powerful method for finding all solutions to a problem. For larger problems, the method performs inconsistently with regard to efficiency, at least when reasonable initial bounds are not provided.

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“…The heart of the extended algorithm, however, is still the original dogleg strategy, because it has superior global convergence properties. The basic algorithm was described by Powell (1970), and the many modifications have been made (for example, Chen and Stadtherr, 1981). The notation we use is similar to that used by Lucia and Xu (1992) for the single variable case.…”

Section: Extended Trust Region Methods In the Complex Domainmentioning

confidence: 99%