Adaptive Barrier Update Strategies for Nonlinear Interior Methods

Nocedal, Jorge; Wächter, Andreas; Waltz, Richard A.

doi:10.1137/060649513

Cited by 90 publications

(70 citation statements)

References 26 publications

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“…changing the initial value of some parameters and especially the barrier parameter, using a less aggressive decrease of the barrier parameter, using an alternative interior-point algorithm, etc.) [16,40], but they take additional computational effort without guaranteeing solution restoration.…”

Section: Discussion Conclusion and Perspectivesmentioning

confidence: 99%

“…Furthermore, the convergence is not restored even after trying few classical heuristic techniques (e.g. different initial values for the barrier parameter , smaller values of the safety parameter , and different initializations of variables) [16,40]. However, by using another IPM algorithm, namely the predictor-corrector (that we generally found slightly less reliable than the MCC algorithm) a locally optimal solution is found.…”

Section: Opf Failure On a Very Tough Problemmentioning

confidence: 99%

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Experiments with the interior-point method for solving large scale Optimal Power Flow problems

Capitanescu

Wehenkel

2013

Electric Power Systems Research

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This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution and sharing with colleagues. and Security-Constrained Optimal Power Flow (SCOPF) problems. The paper discusses transparently the problems encountered such as convergence reliability and speed issues of the method.

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Section: Discussion Conclusion and Perspectivesmentioning

confidence: 99%

Section: Opf Failure On a Very Tough Problemmentioning

confidence: 99%

Experiments with the interior-point method for solving large scale Optimal Power Flow problems

Capitanescu

Wehenkel

2013

Electric Power Systems Research

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“…[43]), where the barrier parameter is fixed until an approximate solution of (64) has been obtained, and there is a variety of dynamic update strategies (cf. [12,36,48,84,96,97,98]). Convergence properties of the Fiacco-McCormick approach have been studied in [28] and [100], whereas a convergence analysis of dynamic update strategies has been addressed in [12,36,84,97].…”

Section: Path-following Barrier Methodsmentioning

confidence: 99%

Multiscale and Multiphysics Aspects in Modeling and Simulation of Surface Acoustic Wave Driven Microfluidic Biochips

Antil¹,

Hoppe²,

Linsenmann³

et al. 2012

Progress in Computational Physics (PiCP) Vol: 2 Coupled Fluid Flow in Energy, Biology and Environmental Research

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Microfluidic biochips are devices that are designed for high throughput screening and hybridization in genomics, protein profiling in proteomics, and cell analysis in cytometry. They are used in clinical diagnostics, pharmaceutics and forensics. The biochips consist of a lithographically produced network of channels and reservoirs on top of a glass or plastic plate. The idea is to transport the injected DNA or protein probes in the amount of nanoliters along the network to a reservoir where the chemical analysis is performed. Conventional biochips use external pumps to generate the fluid flow within the network. A more precise control of the fluid flow can be achieved by piezoelectrically agitated surface acoustic waves (SAW) generated by interdigital transducers on top of the chip, traveling across the surface and entering the fluid filled channels. The fluid and SAW interaction can be described by a mathematical model which consists of a coupling of the piezoelectric equations and the compressible Navier-Stokes equations featuring processes that occur on vastly different time scales. In this contribution, we follow a homogenization approach in order to cope with the multiscale behavior of the coupled system that enables a separate treatment of the fast and slowly varying processes. The resulting model equations are the basis for the numerical simulation which is taken care of by implicit time stepping and finite element discretizations in space. Finally, the need for a better efficiency and cost effectiveness of the SAW driven biochips in the sense of a significant speed-up and more favorable reliability of the hybridization process requires an improved design which will also be addressed in this contribution. In particular, the challenge to deal with the resulting large scale optimal control and optimization problems can be met by the application of projection based model reduction techniques.

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“…X * satisfies K(X * , 0) = 0. It is important to note that, for = 0, exact (X) is the equivalent of quality function in [26].…”

Section: Optimal Centering Parametermentioning

confidence: 99%

“…If the number of corrections less than Step 5. According to (26), update the iteration point by using ΔΧ, and , = + 1, goto Step 1.…”

Section: Algorithm Improved Ipm (I-ipm)mentioning

confidence: 99%

A Novel Separable Model and Decomposition Method for Sensor Locational Decision Problem

Yang

Li²

2014

International Journal of Distributed Sensor Networks

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This paper proposes a new separable model for the sensor locational decision problem covering a line (SLDPCL). By decomposing a multivariate function into several univariate functions, a separable outer approximation methodology that can be used to improve the outer approximation of classical convex programming technique is presented. A novel outer approximation method (OAM) for this proposed separable model is proposed. The algorithm alternates between solving a mixed integer linear program and a convex nonlinear program (NLP). An improved interior point method based on optimal centering parameter is employed to solve the NLP subproblem. The simulation results for test instances that range in size from 10 to 20000 sensors show that the proposed method is fast and robust, and the method is very promising for large-scale SLDPCL problems due to its excellent scalability.

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Adaptive Barrier Update Strategies for Nonlinear Interior Methods

Cited by 90 publications

References 26 publications

Experiments with the interior-point method for solving large scale Optimal Power Flow problems

Experiments with the interior-point method for solving large scale Optimal Power Flow problems

Multiscale and Multiphysics Aspects in Modeling and Simulation of Surface Acoustic Wave Driven Microfluidic Biochips

A Novel Separable Model and Decomposition Method for Sensor Locational Decision Problem

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