Global and local optimization in identification of parabolic systems

2020 ◽  
Vol 28 (6) ◽  
pp. 899-913
Author(s):  
Olga Krivorotko ◽  
Sergey Kabanikhin ◽  
Shuhua Zhang ◽  
Victoriya Kashtanova
Keyword(s):  
Gradient Method ◽  
Online Social Networks ◽  
Optimization Problems ◽  
Initial Conditions ◽  
Gradient Methods ◽  
Parabolic Systems ◽  
Local Optimization ◽  
Solow Model ◽  
Unknown Parameters ◽  
Decomposition Approach

AbstractThe problem of identification of coefficients and initial conditions for a boundary value problem for parabolic equations that reduces to a minimization problem of a misfit function is investigated. Firstly, the tensor train decomposition approach is presented as a global convergence algorithm. The idea of the proposed method is to extract the tensor structure of the optimized functional and use it for multidimensional optimization problems. Secondly, for the refinement of the unknown parameters, three local optimization approaches are implemented and compared: Nelder–Mead simplex method, gradient method of minimum errors, adaptive gradient method. For gradient methods, the evident formula for the continuous gradient of the misfit function is obtained. The identification problem for the diffusive logistic mathematical model which can be applied to social sciences (online social networks), economy (spatial Solow model) and epidemiology (coronavirus COVID-19, HIV, etc.) is considered. The numerical results for information propagation in online social network are presented and discussed.

scholarly journals A Penalized Linear and Nonlinear Combined Conjugate Gradient Method for the Reconstruction of Fluorescence Molecular Tomography

2007 ◽  
Vol 2007 ◽  
pp. 1-19 ◽  
Author(s):  
Shang Shang ◽  
Jing Bai ◽  
Xiaolei Song ◽  
Hongkai Wang ◽  
Jaclyn Lau
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Optimization Problems ◽  
Gradient Methods ◽  
Reconstruction Algorithms ◽  
Fluorescence Molecular Tomography ◽  
Nonlinear Conjugate Gradient Method ◽  
Gradient Based ◽  
Linear And Nonlinear

Conjugate gradient method is verified to be efficient for nonlinear optimization problems of large-dimension data. In this paper, a penalized linear and nonlinear combined conjugate gradient method for the reconstruction of fluorescence molecular tomography (FMT) is presented. The algorithm combines the linear conjugate gradient method and the nonlinear conjugate gradient method together based on a restart strategy, in order to take advantage of the two kinds of conjugate gradient methods and compensate for the disadvantages. A quadratic penalty method is adopted to gain a nonnegative constraint and reduce the illposedness of the problem. Simulation studies show that the presented algorithm is accurate, stable, and fast. It has a better performance than the conventional conjugate gradient-based reconstruction algorithms. It offers an effective approach to reconstruct fluorochrome information for FMT.

scholarly journals A Modified Three-Term Type CD Conjugate Gradient Algorithm for Unconstrained Optimization Problems

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Zhan Wang ◽  
Pengyuan Li ◽  
Xiangrong Li ◽  
Hongtruong Pham
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Optimization Problems ◽  
Gradient Methods ◽  
Trust Region ◽  
Conjugate Gradient Algorithm ◽  
Gradient Algorithm ◽  
General Function ◽  
Term Type

Conjugate gradient methods are well-known methods which are widely applied in many practical fields. CD conjugate gradient method is one of the classical types. In this paper, a modified three-term type CD conjugate gradient algorithm is proposed. Some good features are presented as follows: (i) A modified three-term type CD conjugate gradient formula is presented. (ii) The given algorithm possesses sufficient descent property and trust region property. (iii) The algorithm has global convergence with the modified weak Wolfe–Powell (MWWP) line search technique and projection technique for general function. The new algorithm has made great progress in numerical experiments. It shows that the modified three-term type CD conjugate gradient method is more competitive than the classical CD conjugate gradient method.

Application of Differential Evolution in System Identification of Servo-Hydraulic System With a Flexible Load

2006 ◽  
Author(s):  
H. Yousefi ◽  
H. Handroos
Keyword(s):  
System Identification ◽  
Differential Evolution ◽  
Hydraulic System ◽  
Optimization Problems ◽  
Initial Conditions ◽  
Large Set ◽  
Unknown Parameters ◽  
Nonlinear Constraint ◽  
De Algorithm ◽  
Flexible Load

Electro Hydraulic Servo Systems (EHSS) with an asymmetrical cylinder are commonly used in industry. These kinds of systems are nonlinear in nature and their dynamic equations have several unknown parameters. System identification is a prerequisite to analysis of a dynamic system and design of an appropriate controller for improving its performance. In conventional identification methods, a model structure is selected and the parameters of that model are calculated by optimizing an objective function. This process usually requires a large set of input/output data from the system. In addition, the obtained parameters may be only locally optimal. One of the most promising novel evolutionary algorithms is the Differential Evolution (DE) algorithm for solving global optimization problems with continuous parameters. In this article, the DE algorithm is proposed for handling nonlinear constraint functions with boundary limits of variables to find the best parameters of a nonlinear servo-hydraulic system with flexible load. The DE guarantees Fast speed convergence and accurate solutions regardless the initial conditions of parameters. The results suggest that, DE is useful, reliable and easy to use tools in many aspects of control engineering and especially in system identification.

scholarly journals A Hybrid of DL and WYL Nonlinear Conjugate Gradient Methods

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Shengwei Yao ◽  
Bin Qin
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Optimization Problems ◽  
Gradient Methods ◽  
Test Problems ◽  
Conjugate Gradient Methods ◽  
Sufficient Descent Condition ◽  
Nonlinear Conjugate Gradient ◽  
Nonlinear Conjugate Gradient Methods

The conjugate gradient method is an efficient method for solving large-scale nonlinear optimization problems. In this paper, we propose a nonlinear conjugate gradient method which can be considered as a hybrid of DL and WYL conjugate gradient methods. The given method possesses the sufficient descent condition under the Wolfe-Powell line search and is globally convergent for general functions. Our numerical results show that the proposed method is very robust and efficient for the test problems.

scholarly journals Two Versions of the Spectral Nonlinear Conjugate Gradient Method

2018 ◽  
Vol 29 (1) ◽  
pp. 133
Author(s):  
Basim A. Hassan ◽  
Haneen A. Alashoor
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Optimization Problems ◽  
Gradient Methods ◽  
Convergence Properties ◽  
Nonlinear Conjugate Gradient Method ◽  
Unconstrained Optimization Problems ◽  
Nonlinear Conjugate Gradient ◽  
Nonlinear Conjugate Gradient Methods

The nonlinear conjugate gradient method is widely used to solve unconstrained optimization problems. In this paper the development of different versions of nonlinear conjugate gradient methods with global convergence properties proved. Numerical results indicated that the proposed method is very efficient.

scholarly journals Penalty Algorithm Based on Three-Term Conjugate Gradient Method for Unconstrained Optimization Portfolio Management Problems

2019 ◽  
pp. 1-13
Author(s):  
Samson Akinwale ◽  
O. O. Okundalaye
Keyword(s):  
Unconstrained Optimization ◽  
Conjugate Gradient Method ◽  
Portfolio Management ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Optimization Problems ◽  
Computational Cost ◽  
Gradient Methods ◽  
Unconstrained Optimization Problems ◽  
Management Problems

In a class of solving unconstrained optimization problems, the conjugate gradient method has been proved to be efficient by researchers' due to it's smaller storage requirements and computational cost. Then, a class of penalty algorithms based on three-term conjugate gradient methods was developed and extend to and solution of an unconstrained minimization portfolio management problems, where the objective function is a piecewise quadratic polynomial. By implementing the proposed algorithm to solve some selected unconstrained optimization problems, resulted in improvement in the total number of iterations and CPU time. It was shown that this algorithm is promising.

scholarly journals A Modified Hybrid Conjugate Gradient Method for Unconstrained Optimization

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Minglei Fang ◽  
Min Wang ◽  
Min Sun ◽  
Rong Chen
Keyword(s):  
Unconstrained Optimization ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Large Scale ◽  
Line Search ◽  
Optimization Problems ◽  
Gradient Methods ◽  
Hybrid Conjugate Gradient Method ◽  
Large Scale Unconstrained Optimization

The nonlinear conjugate gradient algorithms are a very effective way in solving large-scale unconstrained optimization problems. Based on some famous previous conjugate gradient methods, a modified hybrid conjugate gradient method was proposed. The proposed method can generate decent directions at every iteration independent of any line search. Under the Wolfe line search, the proposed method possesses global convergence. Numerical results show that the modified method is efficient and robust.

scholarly journals Global convergence analysis of a new hybrid conjugate gradient method for unconstrained optimization problems

2017 ◽  
Vol 13 (2) ◽  
Author(s):  
Ibrahim Abdullahi ◽  
Rohanin Ahmad
Keyword(s):  
Unconstrained Optimization ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Line Search ◽  
Optimization Problems ◽  
Gradient Methods ◽  
Unconstrained Optimization Problems ◽  
Numerical Experimentation ◽  
Hybrid Conjugate Gradient Method

In this paper, we propose a new hybrid conjugate gradient method for unconstrained optimization problems. The proposed method comprises of beta (DY), beta (WHY), beta (RAMI)  and beta (New). The beta (New)  was constructed purposely for this proposed hybrid method.The method possesses sufficient descent property irrespective of the line search. Under Strong Wolfe-Powell line search, we proved that the method is globally convergent. Numerical experimentation shows the effectiveness and robustness of the proposed method when compare with some hybrid as well as some modified conjugate gradient methods.

EFFECTIVENESS OF "SWIM-UP" AND "GRADIENT" METHODS IN SPERM PREPARATION FOR ARTIFICIAL INSEMINATION

2014 ◽  
pp. 25-29
Author(s):  
Minh Tam Le ◽  
Van Trung Nguyen ◽  
Thi Tam An Nguyen ◽  
Quang Trung Phan ◽  
Ngoc Thanh Cao
Keyword(s):  
Gradient Method ◽  
Artificial Insemination ◽  
Sperm Count ◽  
Gradient Methods ◽  
Infertility Treatment ◽  
University Hospital ◽  
Preparation Methods ◽  
Sperm Preparation ◽  
Abnormal Morphology ◽  
Sperm Washing

Objectives: Artificial insemination with sperm preparation and inseminate to the uterus is a common method of infertility treatment. Currently two methods used for sperm washing is “swim-up” and “gradient”. Materials and methods:cross-sectional description in 166 cycles of artificial insemination in Hue University Hospital from April, 2012 to March, 2013 in order to compare effectiveness between “swim-up” and “gradient” methods. Samples were collected randomly into two methods. Results:Results of sperm preparation in both methods are equivalent in terms of the following parameters total sperm count, total number of progressive sperm, total good morphology sperm. However, “gradient” method results in higher number of progressive sperm in case with slow motility (38.3% vs. 26.1%) or abnormal morphology (34.9% vs. 19.7 %) compared with “swim-up” method. Pregnancy rates after artificial insemination were similar between two preparation methods. Conclusion:In case of slow motility sperm and abnormal morphology, “gradient” method should be used to increase the number of progressive sperms. Pregnancy outcome depends on many factors other than preparation methods. Key words: Artificial insemination, sperm preparation, infertility treatment

scholarly journals Design and Automated Optimization of an Internal Turret Mooring System in the Frequency and Time Domain

2021 ◽  
Vol 9 (6) ◽  
pp. 581
Author(s):  
Hongrae Park ◽  
Sungjun Jung
Keyword(s):  
System Design ◽  
Time Domain ◽  
Initial Conditions ◽  
Minimum Weight ◽  
Optimization Algorithms ◽  
Local Optimization ◽  
Mooring System ◽  
Floating Offshore Wind Turbines ◽  
Global And Local Optimization ◽  
Global And Local

A cost-effective mooring system design has been emphasized for traditional offshore industry applications and in the design of floating offshore wind turbines. The industry consensus regarding mooring system design is mainly inhibited by previous project experience. The design of the mooring system also requires a significant number of design cycles. To take aim at these challenges, this paper studies the application of an optimization algorithm to the Floating Production Storage and Offloading (FPSO) mooring system design with an internal turret system at deep-water locations. The goal is to minimize mooring system costs by satisfying constraints, and an objective function is defined as the minimum weight of the mooring system. Anchor loads, a floating body offset and mooring line tensions are defined as constraints. In the process of optimization, the mooring system is analyzed in terms of the frequency domain and time domain, and global and local optimization algorithms are also deployed towards reaching the optimum solution. Three cases are studied with the same initial conditions. The global and local optimization algorithms successfully find a feasible mooring system by reducing the mooring system cost by up to 52%.

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