Book Chapter10.1007/978-1-4612-0839-6_7
A Generalized Reduced Gradient Algorithm for Large-scale Trajectory Optimization Problems
Kathryn E. Brenan,Wayne P. Hallman +1 more
- 01 Jan 1995
- pp 117-132
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TL;DR: This paper focuses on the design of a generalized reduced gradient algorithm to exploit the sparsity structure of the collocation equations.
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Abstract: This paper describes the design of a “sparse” nonlinear programming algorithm for a “large scale” flight optimization and sizing code. This program is designed to solve trajectory optimal control problems with path constraints. The direct transcription technique is applied to discretize an optimal control problem into a sparse, large scale parameter optimization problem for subsequent numerical solution by a nonlinear programming algorithm. This paper focuses on the design of a generalized reduced gradient algorithm to exploit the sparsity structure of the collocation equations.
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Citations
Optimal Design and Control
Jeff Borggaard,John Burkardt,Max D. Gunzburger,Janet S. Peterson +3 more
- 01 Jan 1995
TL;DR: This volume is a collection of papers written by engineers and mathematicians actively involved in innovative research in control and optimization, with emphasis placed on problems governed by partial differential equations.
51
Exploiting Sparsity in the Direct Transcription Method for OptimalControl
John T. Betts,William P. Huffman +1 more
TL;DR: This paper describes how to actually construct the Jacobian and Hessian matrices efficiently, and exploit sparsity inherent in the problem, which can significantly reduce the computational costs when the original optimal control problem has many state and control variables.
27
Development of an Interface Shear Strength Tester and a Model Predicting the Optimal Application Rate of Tack Coat
Dowan Kim,Sungho Mun +1 more
TL;DR: In this paper, the authors used the generalized reduced gradient algorithm to construct a nonlinear predictive function using data from the Interface Shear Strength (ISS) tests to define the optimum application rates (OARs) of tack coat materials generally used in South Korea.
4
Rüzgar enerji̇si̇ güç yoğunluğu tahmi̇ni̇nde opti̇mum wei̇bull olasilik dağilim parametreleri̇ni̇n elde edi̇lmesi̇ i̇çi̇n i̇stati̇sti̇k, matemati̇k ve fi̇zi̇k tabanli algori̇tmalarin karşilaştirmali anali̇zi̇: loras ve foça örnekleri̇
Bayram Köse,Bekir Can Telkenaroğlu,Bahar Demirtürk +2 more
TL;DR: Rüzgar enerjisinin Güç Yönunluğuna Tahmin edilen Weibull Olasılık Dağılım Fonksiyonunun Parametrelerinin Elde Edilmesi için İstatistiks, Matematık ve Fiziğe Taban Algoritmaların Karşuylaştırması Loras ve Foça gözlem istasyonlarında daha iyi sonuçlar verdiği bulunmuştur.
References
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Solving least squares problems
Charles L. Lawson,Richard J. Hanson +1 more
- 01 Jun 1974
TL;DR: Since the lm function provides a lot of features it is rather complicated so it is going to instead use the function lsfit as a model, which computes only the coefficient estimates and the residuals.
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Numerical solution of initial-value problems in differential-algebraic equations
K. E. Brenan,Stephen L. Campbell,Linda R. Petzold +2 more
- 01 Jan 1987
TL;DR: In this article, the authors introduce the theory of DAE's and the index Linear constant coefficient, linear time varying, and nonlinear index systems, as well as a general linear multistep method.
3.3K
Direct trajectory optimization using nonlinear programming and collocation
C. R. Hargraves,Stephen W. Paris +1 more
TL;DR: In this article, an algorithm for the direct numerical solution of an optimal control problem is given, which employs cubic polynomials to represent state variables, linearly interpolates control variables, and uses collocation to satisfy the differential equations.
1.2K