scholarly journals Subspace Methods for Nonlinear Optimization

2021 ◽  
Vol 2 (4) ◽  
pp. 585-651
Author(s):  
Xin Liu
Author(s):  
Ahmed Abdalla ◽  
Suhad Mohammed ◽  
Tang Bin ◽  
Jumma Mary Atieno ◽  
Abdelazeim Abdalla

This paper considers the problem of estimating the direction of arrival (DOA) for the both incoherent and coherent signals from narrowband sources, located in the far field in the case of uniform linear array sensors. Three different methods are analyzed. Specifically, these methods are Music, Root-Music and ESPRIT. The pros and cons of these methods are identified and compared in light of different viewpoints. The performance of the three methods is evaluated, analytically, when possible, and by Matlab simulation. This paper can be a roadmap for beginners in understanding the basic concepts of DOA estimation issues, properties and performance.


Author(s):  
Christodoulos A. Floudas

Filling a void in chemical engineering and optimization literature, this book presents the theory and methods for nonlinear and mixed-integer optimization, and their applications in the important area of process synthesis. Other topics include modeling issues in process synthesis, and optimization-based approaches in the synthesis of heat recovery systems, distillation-based systems, and reactor-based systems. The basics of convex analysis and nonlinear optimization are also covered and the elementary concepts of mixed-integer linear optimization are introduced. All chapters have several illustrations and geometrical interpretations of the material as well as suggested problems. Nonlinear and Mixed-Integer Optimization will prove to be an invaluable source--either as a textbook or a reference--for researchers and graduate students interested in continuous and discrete nonlinear optimization issues in engineering design, process synthesis, process operations, applied mathematics, operations research, industrial management, and systems engineering.


1999 ◽  
Vol 9 (3) ◽  
pp. 755-778 ◽  
Author(s):  
Paul T. Boggs ◽  
Anthony J. Kearsley ◽  
Jon W. Tolle

Author(s):  
Yuka Hashimoto ◽  
Takashi Nodera

AbstractThe Krylov subspace method has been investigated and refined for approximating the behaviors of finite or infinite dimensional linear operators. It has been used for approximating eigenvalues, solutions of linear equations, and operator functions acting on vectors. Recently, for time-series data analysis, much attention is being paid to the Krylov subspace method as a viable method for estimating the multiplications of a vector by an unknown linear operator referred to as a transfer operator. In this paper, we investigate a convergence analysis for Krylov subspace methods for estimating operator-vector multiplications.


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