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Optimization on the real symplectic group

MONATSHEFTE FUR MATHEMATIK 2020年第3期191卷 465-485页

作者： Birtea, Petre Casu, Ioan Comanescu, Dan West Univ Timisoara Dept Math Bd Vasile Parvan 4 RO-300223 Timisoara Romania

We regard the real symplectic group Sp(2n,R)\documentclass[12pt] as a constraint submanifold of the 2nx2n\documentclass[12pt] real matrices M2n(R)\documentclass[12pt] endowed with the Euclidean (Frobenius) metric, respectively as a submanifold of the general linear group Gl(2n,R)\documentclass[12pt] endowed with the (left) invariant metric. For a cost function that defines an optimization problem on the real symplectic group we give a necessary and sufficient condition for critical points and we apply this condition to the particular case of a least square cost function. In order to characterize the critical points we give a formula for the Hessian of a cost function defined on the real symplectic group, with respect to both considered metrics. For a generalized Brockett cost function we present a necessary condition and a sufficient condition for local minimum. We construct a retraction map that allows us to detail the steepest descent and embedded Newton algorithms for solving an optimization problem on the real symplectic group.

关键词： Optimization Constraint manifold Real symplectic group Retraction map steepest descent algorithm Newton algorithm

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Exit wave reconstruction of a focal series of images with structural changes in high-resolution transmission electron microscopy

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JOURNAL OF MICROSCOPY 2024年第1期296卷 24-33页

作者： Zhang, Xiaohan Chen, Shaowen Wang, Shuya Huang, Ying Jin, Chuanhong Lin, Fang South China Agr Univ Coll Elect Engn Dept Appl Phys Guangzhou Guangdong Peoples R China Jihua Lab Foshan Guangdong Peoples R China Zhuhai Multiplier Informat Technol Co Ltd Dept Res & Dev Zhuhai Guangdong Peoples R China Zhejiang Univ Sch Mat Sci & Engn State Key Lab Silicon & Adv Semicond Mat Hangzhou Peoples R China South China Agr Univ Coll Elect Engn Guangzhou 510642 Guangdong Peoples R China

High-resolution transmission electron microscopy (HRTEM) images can capture the atomic-resolution details of the dynamically changing structure of nanomaterials. Here, we propose a new scheme and an improved reconstruction algorithm to reconstruct the exit wave function for each image in a focal series of HRTEM images to reveal structural changes. In this scheme, the wave reconstructed from the focal series of images is treated as the initial wave in the reconstruction process for each HRTEM image. Additionally, to suppress noise at the frequencies where the signal is weak due to the modulation of the lens transfer function, a weight factor is introduced in the improved reconstruction algorithm. The advantages of the new scheme and algorithms are validated by using the HRTEM images of a natural specimen and a single-layer molybdenum disulphide. This algorithm enables image resolution enhancement and lens aberration removal, while potentially allowing the visualisation of the structural evolution of nanostructures.

关键词： backpropagation algorithm exit wave function reconstruction high-resolution transmission electron microscopy steepest descent algorithm

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Novel Least Mean Square algorithm Using First order Al-Alaoui Digital Differentiator

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NATIONAL ACADEMY SCIENCE LETTERS-INDIA 2018年第4期41卷 215-218页

作者： Krishna, B. T. Jawaharlal Nehru Technol Univ Kakinada Univ Coll Engn Kakinada Dept Elect & Commun Engn Kakinada 533003 Andhra Prades India

This paper proposes a Novel least mean square algorithm using First order Al-Alaoui *** performance of the proposed algorithm is compared with existing algorithms by taking an example. The results prove the efficacy o... 详细信息

关键词： Digital differentiator Adaptive filters steepest descent algorithm LMS algorithm System identification etc.

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Space mapping for optimal control of a nonisothermal tube drawing process

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MATHEMATICAL METHODS IN THE APPLIED SCIENCES 2021年第15期44卷 11797-11809页

作者： Butt, Azhar Iqbal Kashif Mumtaz, Kinza Resendiz-Flores, Edgar O. Govt Coll Univ Lahore Dept Math Lahore Pakistan Lahore Univ Management Sci Dept Math Lahore Pakistan Technol Inst Saltillo Dept Metal Mech Engn Div Postgrad Studies & Res Saltillo 25280 Coahuila Mexico

We implement space mapping technique for the first time to optimize geometry of a glass tube during its production process. The strategy is to align the optimizer of the coarse model (isothermal tube drawing) with the fine model (nonisothermal tube drawing) through space mapping technique in order to find an optimal solution of a control problem. Adjoint variable approach is used to find optimizer of the coarse model. Numerical results obtained through aggressive space mapping (ASM) algorithm are presented and discussed.

关键词： aggressive space mapping algorithm coarse model fine model glass tube drawing process space mapping steepest descent algorithm

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The relaxation of non-quasiconvex variational integrals

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NUMERISCHE MATHEMATIK 1999年第2期82卷 281-311页

作者： Kloucek, P Rice Univ Dept Computat & Appl Math Houston TX 77005 USA

We show that the steepest descent algorithm in connection with wiggly energies yields minimizing sequences that converge to a global minimum of the associated non-quasiconvex variational integrals. We introduce a multi-level infinite dimensional variant of the steepest descent algorithm designed to compute complex microstructures by forming nonsmooth minimizers from the smooth initial guesses. We apply this multilevel method to the minimization of the variational problems associated with martensitic branching.

关键词： steepest descent algorithm Minimise MARTENSITE Global Minimum Integral equations Converge

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On the asymptotically stochastic computational modeling of microstructures

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FUTURE GENERATION COMPUTER SYSTEMS 2004年第3期20卷 409-424页

作者： Cox, DD Kloucek, P Reynolds, DR Rice Univ Dept Computat & Appl Math Houston TX 77005 USA Rice Univ Dept Stat Houston TX 77005 USA

We consider a class of alloys and ceramics with equilibria described by non-attainable infima of non-quasiconvex variational integrals. Such situations frequently arise when atomic lattice structure plays an important role at the mesoscopic continuum level. We prove that standard variational approaches associated with gradient based relaxation of non-quasiconvex integrals in Banach or Hilbert spaces are not capable of generating relaxing sequences for problems with non-attainable structure. We introduce a variational principle suitable for the computational purposes of approaching non-attainable infima of variational integrals. We demonstrate that this principle is suitable for direct calculations of the Young Measures on a computational example in one dimension. The new variational principle provides the possibility to approximate crystalline microstructures using a Fokker-Planck equation at the meso-scale. We provide an example of such a construction. (C) 2003 Elsevier B.V. All rights reserved.

关键词： microstructures crystalline materials weak white noise steepest descent algorithm weak convergence calculus of variations

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Hereditary systems and greedy-type algorithms

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DISCRETE APPLIED MATHEMATICS 2003年第1-3期132卷 137-148页

作者： Il'ev, V Omsk State Univ Dept Math Omsk 644077 Russia

We define a hereditary system on a finite set U as a partition of the family 2(U) of all subsets of U into disjoint families A and D satisfying (A is an element of V, A' subset of or equal to A) double right arrow A' is an element of A and (D is an element of D, D subset of or equal to D') = double right arrow D' is an element of D, respectively. The members of A are called independent sets, the sets D is an element of D are called dependent. We consider two important special cases of hereditary systems, matroids and comatroids, and study the structure of these objects. Two general combinatorial optimization problems on a hereditary system, the maximum independent set problem max{f (X): X is an element of A} and the minimum dependent set problem min{f(X): X is an element of D}, are considered. Jenkyns, Korte and Hausmann obtained a performance guarantee of the greedy heuristic ('best in') for the maximum independent set problem. We present a greedy-type approximation algorithm for solving the minimum dependent set problem, the steepest descent heuristic ('worst out'), study interconnections between the above-mentioned problems and derive performance guarantees of the steepest descent algorithm. Finally, we apply our results to obtain performance guarantees of the steepest descent algorithm for some known special combinatorial minimization problems. (C) 2003 Elsevier B.V. All rights reserved.

关键词： hereditary system comatroid steepest descent algorithm performance guarantee

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Method for Solving the Pilot Optimal Attention Allocation Problem 2

Method for Solving the Pilot Optimal Attention Allocation Pr...

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2nd IEEE International Conference on Progress in Informatics and Computing (PIC)

作者： Liu, Shuang Wanyan, Xiaoru Zhuang, Damin Beihang Univ Sch Aeronaut Sci & Engn Beijing 100191 Peoples R China

ISBN: (纸本)9781479920303

According to the modern control and optimal estimation theory, a mathematical model of the pilot attention resource allocation is developed. This model analyzes the inherent characteristics of pilot input and output links in the pilot-vehicle closed-loop system, and the optimal control model of pilot is established by simplification and mathematical modeling. The control task chosen in this paper concerns the longitudinal motion of a hovering aircraft. To solve the pilot optimal attention allocation problem in the instrument-monitoring task of the pilot-vehicle closed-loop system an objective function is set up based on flight control system state equation. In the process of solving optimization problem, the constrained optimization problem is converted into an unconstrained problem, and is solved effectively with the method of steepest descent algorithm in the MATLAB.

关键词： pilot attention allocation optimal control model ergonomics steepest descent algorithm

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A Novel Autocalibration of 3-Axis MEMS Accelerometers Based on Improved PSO algorithm

A Novel Autocalibration of 3-Axis MEMS Accelerometers Based ...

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7th International Conference on MEMS, NANO and Smart Systems (ICMENS 2011)

作者： Liu, Renhao Wang, Hua Beijing Univ Aeronaut & Astronaut Sch Astronaut Beijing 100083 Peoples R China

ISBN: (纸本)9783037853122

This paper presents a novel procedure to calibrate the strap-down 3-axis MEMS accelerometers for UAV navigat-ion. Firstly, we establish an explicit calibration model with the measurement values of accelerometers, where the calibration is realized via geometric transformations. Secondly, the transfor-mation parameters are calculated through particle swarm optimization (PSO). For the problem of slower convergence rates near the global optimum, the classical PSO algorithm is improved. Based on the numerical optimization idea, the steepest descent method is introduced to PSO. The parameters are searched in the rough by adopting PSO and the precision ones are found by using steepest descent method. Then, the optimal transformation is achieved by the minimum distance function based on this improved PSO(IPSO) algorithm. Finally, the calibration procedure is tested by comparing the attitude produced by the 3-axis accelerometers with that measured by a turntable. The results show that the IPSO algorithm can significantly improve the performance of the classical PSO algorithm, and the maximum attitude error is reduced to 6% of that before calibration. In addition, the proposed procedure does not rely on prior knowledge of the accelerometers and any equipment. So, it is suitable for calibration in field. Such a method is especially useful in UAV applications.

关键词： MEMS Accelerometer Calibration Particle swarm optimization steepest descent algorithm

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Novel Least Mean Square algorithm

Novel Least Mean Square Algorithm

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International Symposium on Intelligent Signal Processing and Communication Systems (ISPACS)

作者： Krishna, B. T. Jawaharlal Nehru Technol Univ Kakinada Univ Coll Engn Vizianagaram Dept Elect & Commun Engn Vizianagaram 535003 Andhra Pradesh India

A Novel Least Mean Square(LMS) algorithm using First order Al-Alaoui differentiator is proposed. The condition for stability is also derived. The performance of the novel technique is compared with existing algorithms... 详细信息

ISBN: (纸本)9781509006298

关键词： Digital differentiator Adaptive Filters steepest descent algorithm LMS algorithm System Identification

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