In this paper,we propose a three-term conjugate gradient method for solving unconstrained optimization problems based on the Hestenes-Stiefel(HS)conjugate gradient method and Polak-Ribiere-Polyak(PRP)conjugate gradien...In this paper,we propose a three-term conjugate gradient method for solving unconstrained optimization problems based on the Hestenes-Stiefel(HS)conjugate gradient method and Polak-Ribiere-Polyak(PRP)conjugate gradient method.Under the condition of standard Wolfe line search,the proposed search direction is the descent direction.For general nonlinear functions,the method is globally convergent.Finally,numerical results show that the proposed method is efficient.展开更多
This paper puts forward a two-parameter family of nonlinear conjugate gradient(CG)method without line search for solving unconstrained optimization problem.The main feature of this method is that it does not rely on a...This paper puts forward a two-parameter family of nonlinear conjugate gradient(CG)method without line search for solving unconstrained optimization problem.The main feature of this method is that it does not rely on any line search and only requires a simple step size formula to always generate a sufficient descent direction.Under certain assumptions,the proposed method is proved to possess global convergence.Finally,our method is compared with other potential methods.A large number of numerical experiments show that our method is more competitive and effective.展开更多
As a generalization of the two-term conjugate gradient method(CGM),the spectral CGM is one of the effective methods for solving unconstrained optimization.In this paper,we enhance the JJSL conjugate parameter,initiall...As a generalization of the two-term conjugate gradient method(CGM),the spectral CGM is one of the effective methods for solving unconstrained optimization.In this paper,we enhance the JJSL conjugate parameter,initially proposed by Jiang et al.(Computational and Applied Mathematics,2021,40:174),through the utilization of a convex combination technique.And this improvement allows for an adaptive search direction by integrating a newly constructed spectral gradient-type restart strategy.Then,we develop a new spectral CGM by employing an inexact line search to determine the step size.With the application of the weak Wolfe line search,we establish the sufficient descent property of the proposed search direction.Moreover,under general assumptions,including the employment of the strong Wolfe line search for step size calculation,we demonstrate the global convergence of our new algorithm.Finally,the given unconstrained optimization test results show that the new algorithm is effective.展开更多
Based on the analysis of the conjugate gradient algorithm, we implement a threedimensional （3D） conjugate gradient inversion algorithm with magnetotelluric impedance data. During the inversion process, the 3D conjug...Based on the analysis of the conjugate gradient algorithm, we implement a threedimensional （3D） conjugate gradient inversion algorithm with magnetotelluric impedance data. During the inversion process, the 3D conjugate gradient inversion algorithm doesn＇ t need to compute and store the Jacobian matrix but directly updates the model from the computation of the Jacobian matrix. Requiring only one forward and four pseudo-forward modeling applications per frequency to produce the model update at each iteration, this algorithm efficiently reduces the computation of the inversion. From a trial inversion with synthetic magnetotelluric data, the validity and stability of the 3D conjugate gradient inversion algorithm is verified.展开更多
In seismic data processing, blind deconvolution is a key technology. Introduced in this paper is a flow of one kind of blind deconvolution. The optimal precondition conjugate gradients (PCG) in Kyrlov subspace is als...In seismic data processing, blind deconvolution is a key technology. Introduced in this paper is a flow of one kind of blind deconvolution. The optimal precondition conjugate gradients (PCG) in Kyrlov subspace is also used to improve the stability of the algorithm. The computation amount is greatly decreased.展开更多
Although conventional reverse time migration can be perfectly applied to structural imaging it lacks the capability of enabling detailed delineation of a lithological reservoir due to irregular illumination. To obtain...Although conventional reverse time migration can be perfectly applied to structural imaging it lacks the capability of enabling detailed delineation of a lithological reservoir due to irregular illumination. To obtain reliable reflectivity of the subsurface it is necessary to solve the imaging problem using inversion. The least-square reverse time migration （LSRTM） （also known as linearized refleetivity inversion） aims to obtain relatively high-resolution amplitude preserving imaging by including the inverse of the Hessian matrix. In practice, the conjugate gradient algorithm is proven to be an efficient iterative method for enabling use of LSRTM. The velocity gradient can be derived from a cross-correlation between observed data and simulated data, making LSRTM independent of wavelet signature and thus more robust in practice. Tests on synthetic and marine data show that LSRTM has good potential for use in reservoir description and four-dimensional （4D） seismic images compared to traditional RTM and Fourier finite difference （FFD） migration. This paper investigates the first order approximation of LSRTM, which is also known as the linear Born approximation. However, for more complex geological structures a higher order approximation should be considered to improve imaging quality.展开更多
Fast solving large-scale linear equations in the finite element analysis is a classical subject in computational mechanics. It is a key technique in computer aided engineering （CAE） and computer aided manufacturing ...Fast solving large-scale linear equations in the finite element analysis is a classical subject in computational mechanics. It is a key technique in computer aided engineering （CAE） and computer aided manufacturing （CAM）. This paper presents a high-efficiency improved symmetric successive over-relaxation （ISSOR） preconditioned conjugate gradient （PCG） method, which maintains lelism consistent with the original form. Ideally, the by 50% as compared with the original algorithm. the convergence and inherent paralcomputation can It is suitable for be reduced nearly high-performance computing with its inherent basic high-efficiency operations. By comparing with the numerical results, it is shown that the proposed method has the best performance.展开更多
The electronic structure of GaAs/Al xGa 1-x As superlattices has been investigated by an ab initio calculation method—the conjugate gradient (CG) approach.In order to determine that,a conventional CG scheme is m...The electronic structure of GaAs/Al xGa 1-x As superlattices has been investigated by an ab initio calculation method—the conjugate gradient (CG) approach.In order to determine that,a conventional CG scheme is modified for our superlattices:First,apart from the former scheme,for the fixed electron density n(z),the eigenvalues and eigenfunctions are calculated,and then by using those,reconstruct the new n(z).Also,for every k z,we apply the CG schemes independently.The calculated energy difference between two minibands,and Fermi energy are in good agreement with the experimental data.展开更多
Based on the analysis of impedance tensor data, tipper data, and the conjugate gradient algorithm, we develop a three-dimensional (3D) conjugate gradient algorithm for inverting magnetotelluric full information data d...Based on the analysis of impedance tensor data, tipper data, and the conjugate gradient algorithm, we develop a three-dimensional (3D) conjugate gradient algorithm for inverting magnetotelluric full information data determined from five electric and magnetic field components and discuss the method to use the full information data for quantitative interpretation of 3D inversion results. Results from the 3D inversion of synthetic data indicate that the results from inverting full information data which combine the impedance tensor and tipper data are better than results from inverting only the impedance tensor data (or tipper data) in improving resolution and reliability. The synthetic examples also demonstrate the validity and stability of this 3D inversion algorithm.展开更多
With the continuous development of full tensor gradiometer （FTG） measurement techniques, three-dimensional （3D） inversion of FTG data is becoming increasingly used in oil and gas exploration. In the fast processin...With the continuous development of full tensor gradiometer （FTG） measurement techniques, three-dimensional （3D） inversion of FTG data is becoming increasingly used in oil and gas exploration. In the fast processing and interpretation of large-scale high-precision data, the use of the graphics processing unit process unit （GPU） and preconditioning methods are very important in the data inversion. In this paper, an improved preconditioned conjugate gradient algorithm is proposed by combining the symmetric successive over-relaxation （SSOR） technique and the incomplete Choleksy decomposition conjugate gradient algorithm （ICCG）. Since preparing the preconditioner requires extra time, a parallel implement based on GPU is proposed. The improved method is then applied in the inversion of noise- contaminated synthetic data to prove its adaptability in the inversion of 3D FTG data. Results show that the parallel SSOR-ICCG algorithm based on NVIDIA Tesla C2050 GPU achieves a speedup of approximately 25 times that of a serial program using a 2.0 GHz Central Processing Unit （CPU）. Real airbome gravity-gradiometry data from Vinton salt dome （south- west Louisiana, USA） are also considered. Good results are obtained, which verifies the efficiency and feasibility of the proposed parallel method in fast inversion of 3D FTG data.展开更多
Large-scale multi-objective optimization problems(LSMOPs)pose challenges to existing optimizers since a set of well-converged and diverse solutions should be found in huge search spaces.While evolutionary algorithms a...Large-scale multi-objective optimization problems(LSMOPs)pose challenges to existing optimizers since a set of well-converged and diverse solutions should be found in huge search spaces.While evolutionary algorithms are good at solving small-scale multi-objective optimization problems,they are criticized for low efficiency in converging to the optimums of LSMOPs.By contrast,mathematical programming methods offer fast convergence speed on large-scale single-objective optimization problems,but they have difficulties in finding diverse solutions for LSMOPs.Currently,how to integrate evolutionary algorithms with mathematical programming methods to solve LSMOPs remains unexplored.In this paper,a hybrid algorithm is tailored for LSMOPs by coupling differential evolution and a conjugate gradient method.On the one hand,conjugate gradients and differential evolution are used to update different decision variables of a set of solutions,where the former drives the solutions to quickly converge towards the Pareto front and the latter promotes the diversity of the solutions to cover the whole Pareto front.On the other hand,objective decomposition strategy of evolutionary multi-objective optimization is used to differentiate the conjugate gradients of solutions,and the line search strategy of mathematical programming is used to ensure the higher quality of each offspring than its parent.In comparison with state-of-the-art evolutionary algorithms,mathematical programming methods,and hybrid algorithms,the proposed algorithm exhibits better convergence and diversity performance on a variety of benchmark and real-world LSMOPs.展开更多
We developed a three-dimensional（3D） conjugate gradient inversion algorithm for in-verting magnetotelluric impedance tensor measurements.In order to show the importance of including diagonal components of magnetotel...We developed a three-dimensional（3D） conjugate gradient inversion algorithm for in-verting magnetotelluric impedance tensor measurements.In order to show the importance of including diagonal components of magnetotelluric impedance tensor in 3D inversion,synthetic data were inverted using the 3D conjugate gradient inversion,and the inversion results were compared and analyzed.The results from the 3D inversion of synthetic data indicate that both the off-diagonal and the diagonal components are required in inversions to obtain better inversion results when there are no enough data sites to recover the target resistivity structure.These examples show that lots of information about 3D structure is also contained in the diagonal components;as a result,diagonal components should be in-cluded in 3D inversions.The inversion algorithm was also used to invert the impedance tensor data ac-quired in the Kayabe area in Japan.Inversions with the synthetic and real data demonstrated the va-lidity and practicability of the inversion algorithm.展开更多
With the development of computational power, there has been an increased focus on data-fitting related seismic inversion techniques for high fidelity seismic velocity model and image, such as full-waveform inversion a...With the development of computational power, there has been an increased focus on data-fitting related seismic inversion techniques for high fidelity seismic velocity model and image, such as full-waveform inversion and least squares migration. However, though more advanced than conventional methods, these data fitting methods can be very expensive in terms of computational cost. Recently, various techniques to optimize these data-fitting seismic inversion problems have been implemented to cater for the industrial need for much improved efficiency. In this study, we propose a general stochastic conjugate gradient method for these data-fitting related inverse problems. We first prescribe the basic theory of our method and then give synthetic examples. Our numerical experiments illustrate the potential of this method for large-size seismic inversion application.展开更多
A hybridization of the three–term conjugate gradient method proposed by Zhang et al. and the nonlinear conjugate gradient method proposed by Polak and Ribi`ere, and Polyak is suggested. Based on an eigenvalue analysi...A hybridization of the three–term conjugate gradient method proposed by Zhang et al. and the nonlinear conjugate gradient method proposed by Polak and Ribi`ere, and Polyak is suggested. Based on an eigenvalue analysis, it is shown that search directions of the proposed method satisfy the sufficient descent condition, independent of the line search and the objective function convexity. Global convergence of the method is established under an Armijo–type line search condition. Numerical experiments show practical efficiency of the proposed method.展开更多
In this paper,an efficient conjugate gradient method is given to solve the general unconstrained optimization problems,which can guarantee the sufficient descent property and the global convergence with the strong Wol...In this paper,an efficient conjugate gradient method is given to solve the general unconstrained optimization problems,which can guarantee the sufficient descent property and the global convergence with the strong Wolfe line search conditions.Numerical results show that the new method is efficient and stationary by comparing with PRP＋ method,so it can be widely used in scientific computation.展开更多
Conjugate gradient optimization algorithms depend on the search directions with different choices for the parameters in the search directions. In this note, by combining the nice numerical performance of PR and HS met...Conjugate gradient optimization algorithms depend on the search directions with different choices for the parameters in the search directions. In this note, by combining the nice numerical performance of PR and HS methods with the global convergence property of the class of conjugate gradient methods presented by HU and STOREY(1991), a class of new restarting conjugate gradient methods is presented. Global convergences of the new method with two kinds of common line searches, are proved. Firstly, it is shown that, using reverse modulus of continuity function and forcing function, the new method for solving unconstrained optimization can work for a continously dif ferentiable function with Curry-Altman's step size rule and a bounded level set. Secondly, by using comparing technique, some general convergence properties of the new method with other kind of step size rule are established. Numerical experiments show that the new method is efficient by comparing with FR conjugate gradient method.展开更多
In this note,by combining the nice numerical performance of PR and HS methods with the global convergence property of FR method,a class of new restarting three terms conjugate gradient methods is presented.Global conv...In this note,by combining the nice numerical performance of PR and HS methods with the global convergence property of FR method,a class of new restarting three terms conjugate gradient methods is presented.Global convergence properties of the new method with two kinds of common line searches are proved.展开更多
Many methods have been put forward to solve unconstrained optimization problems,among which conjugate gradient method(CG)is very important.With the increasing emergence of large⁃scale problems,the subspace technology ...Many methods have been put forward to solve unconstrained optimization problems,among which conjugate gradient method(CG)is very important.With the increasing emergence of large⁃scale problems,the subspace technology has become particularly important and widely used in the field of optimization.In this study,a new CG method was put forward,which combined subspace technology and a cubic regularization model.Besides,a special scaled norm in a cubic regularization model was analyzed.Under certain conditions,some significant characteristics of the search direction were given and the convergence of the algorithm was built.Numerical comparisons show that for the 145 test functions under the CUTEr library,the proposed method is better than two classical CG methods and two new subspaces conjugate gradient methods.展开更多
In [3] Liu et al. investigated global convergence of conjugate gradient methods. In that paper they allowed βκ to be selected in a wider range and the global convergence of the corresponding algorithm without suffic...In [3] Liu et al. investigated global convergence of conjugate gradient methods. In that paper they allowed βκ to be selected in a wider range and the global convergence of the corresponding algorithm without sufficient decrease condition was proved. This paper investigates global convergence of nonmonotone conjugate gradient method under the same conditions.展开更多
Nonlinear conjugate gradient methods have played an important role in solving large scale unconstrained optimi-zation problems,it is characterized by the simplicity of their iteration and their low memory requirements...Nonlinear conjugate gradient methods have played an important role in solving large scale unconstrained optimi-zation problems,it is characterized by the simplicity of their iteration and their low memory requirements.It is well-known that the direction generated by a conjugate gradient method may be not a descent direction.In this paper,a new class of nonlinear conjugate gradient method is presented,its search direction is a descent direction for the objective function.If the objective function is differentiable and its gradient is Lipschitz continuous,the line sbarch satisfies strong Wolfe condition,the global convergence result is established.展开更多
基金Supported by the Science and Technology Project of Guangxi(Guike AD23023002)。
文摘In this paper,we propose a three-term conjugate gradient method for solving unconstrained optimization problems based on the Hestenes-Stiefel(HS)conjugate gradient method and Polak-Ribiere-Polyak(PRP)conjugate gradient method.Under the condition of standard Wolfe line search,the proposed search direction is the descent direction.For general nonlinear functions,the method is globally convergent.Finally,numerical results show that the proposed method is efficient.
基金Supported by 2023 Inner Mongolia University of Finance and Economics,General Scientific Research for Universities directly under Inner Mon‐golia,China (NCYWT23026)2024 High-quality Research Achievements Cultivation Fund Project of Inner Mongolia University of Finance and Economics,China (GZCG2479)。
文摘This paper puts forward a two-parameter family of nonlinear conjugate gradient(CG)method without line search for solving unconstrained optimization problem.The main feature of this method is that it does not rely on any line search and only requires a simple step size formula to always generate a sufficient descent direction.Under certain assumptions,the proposed method is proved to possess global convergence.Finally,our method is compared with other potential methods.A large number of numerical experiments show that our method is more competitive and effective.
基金supported by the National Natural Science Foundation of China(No.72071202)the Key Laboratory of Mathematics and Engineering Applications,Ministry of Education。
文摘As a generalization of the two-term conjugate gradient method(CGM),the spectral CGM is one of the effective methods for solving unconstrained optimization.In this paper,we enhance the JJSL conjugate parameter,initially proposed by Jiang et al.(Computational and Applied Mathematics,2021,40:174),through the utilization of a convex combination technique.And this improvement allows for an adaptive search direction by integrating a newly constructed spectral gradient-type restart strategy.Then,we develop a new spectral CGM by employing an inexact line search to determine the step size.With the application of the weak Wolfe line search,we establish the sufficient descent property of the proposed search direction.Moreover,under general assumptions,including the employment of the strong Wolfe line search for step size calculation,we demonstrate the global convergence of our new algorithm.Finally,the given unconstrained optimization test results show that the new algorithm is effective.
基金sponsored by National Natural Science Foundation of China (Grant Nos. 40774029, 40674037, and 40374024)the National Hi-tech Research and Development Program of China (863 Program) (No. 2007AA09Z310)the Program for New Century Excellent Talents in University (NCET).
文摘Based on the analysis of the conjugate gradient algorithm, we implement a threedimensional （3D） conjugate gradient inversion algorithm with magnetotelluric impedance data. During the inversion process, the 3D conjugate gradient inversion algorithm doesn＇ t need to compute and store the Jacobian matrix but directly updates the model from the computation of the Jacobian matrix. Requiring only one forward and four pseudo-forward modeling applications per frequency to produce the model update at each iteration, this algorithm efficiently reduces the computation of the inversion. From a trial inversion with synthetic magnetotelluric data, the validity and stability of the 3D conjugate gradient inversion algorithm is verified.
基金With the support of the key project of Knowledge Innovation, CAS(KZCX1-y01, KZCX-SW-18), Fund of the China National Natural Sciences and the Daqing Oilfield with Grant No. 49894190
文摘In seismic data processing, blind deconvolution is a key technology. Introduced in this paper is a flow of one kind of blind deconvolution. The optimal precondition conjugate gradients (PCG) in Kyrlov subspace is also used to improve the stability of the algorithm. The computation amount is greatly decreased.
基金sponsored by The National Natural Science Fund(No.41574098)Sinopec Geophysical Key Laboratory Open Fund(No.wtyjy-wx2016-04-2)
文摘Although conventional reverse time migration can be perfectly applied to structural imaging it lacks the capability of enabling detailed delineation of a lithological reservoir due to irregular illumination. To obtain reliable reflectivity of the subsurface it is necessary to solve the imaging problem using inversion. The least-square reverse time migration （LSRTM） （also known as linearized refleetivity inversion） aims to obtain relatively high-resolution amplitude preserving imaging by including the inverse of the Hessian matrix. In practice, the conjugate gradient algorithm is proven to be an efficient iterative method for enabling use of LSRTM. The velocity gradient can be derived from a cross-correlation between observed data and simulated data, making LSRTM independent of wavelet signature and thus more robust in practice. Tests on synthetic and marine data show that LSRTM has good potential for use in reservoir description and four-dimensional （4D） seismic images compared to traditional RTM and Fourier finite difference （FFD） migration. This paper investigates the first order approximation of LSRTM, which is also known as the linear Born approximation. However, for more complex geological structures a higher order approximation should be considered to improve imaging quality.
基金Project supported by the National Natural Science Foundation of China(Nos.5130926141030747+3 种基金41102181and 51121005)the National Basic Research Program of China(973 Program)(No.2011CB013503)the Young Teachers’ Initial Funding Scheme of Sun Yat-sen University(No.39000-1188140)
文摘Fast solving large-scale linear equations in the finite element analysis is a classical subject in computational mechanics. It is a key technique in computer aided engineering （CAE） and computer aided manufacturing （CAM）. This paper presents a high-efficiency improved symmetric successive over-relaxation （ISSOR） preconditioned conjugate gradient （PCG） method, which maintains lelism consistent with the original form. Ideally, the by 50% as compared with the original algorithm. the convergence and inherent paralcomputation can It is suitable for be reduced nearly high-performance computing with its inherent basic high-efficiency operations. By comparing with the numerical results, it is shown that the proposed method has the best performance.
基金Supported by National Natural Science Foundation of China(No.50 0 72 0 1 5 and No.5980 1 0 0 6) and Tianjin Youth Foundation o
文摘The electronic structure of GaAs/Al xGa 1-x As superlattices has been investigated by an ab initio calculation method—the conjugate gradient (CG) approach.In order to determine that,a conventional CG scheme is modified for our superlattices:First,apart from the former scheme,for the fixed electron density n(z),the eigenvalues and eigenfunctions are calculated,and then by using those,reconstruct the new n(z).Also,for every k z,we apply the CG schemes independently.The calculated energy difference between two minibands,and Fermi energy are in good agreement with the experimental data.
基金supported by the National Hi-tech Research and Development Program of China(863Program)(No.2007AA09Z310) National Natural Science Foundation of China(Grant No.40774029 40374024)+1 种基金 the Fundamental Research Funds for the Central Universities(Grant No.2010ZY53) the Program for New Century Excellent Talents in University(NCET)
文摘Based on the analysis of impedance tensor data, tipper data, and the conjugate gradient algorithm, we develop a three-dimensional (3D) conjugate gradient algorithm for inverting magnetotelluric full information data determined from five electric and magnetic field components and discuss the method to use the full information data for quantitative interpretation of 3D inversion results. Results from the 3D inversion of synthetic data indicate that the results from inverting full information data which combine the impedance tensor and tipper data are better than results from inverting only the impedance tensor data (or tipper data) in improving resolution and reliability. The synthetic examples also demonstrate the validity and stability of this 3D inversion algorithm.
基金the Sub-project of National Science and Technology Major Project of China(No.2016ZX05027-002-003)the National Natural Science Foundation of China(No.41404089)+1 种基金the State Key Program of National Natural Science of China(No.41430322)the National Basic Research Program of China(973 Program)(No.2015CB45300)
文摘With the continuous development of full tensor gradiometer （FTG） measurement techniques, three-dimensional （3D） inversion of FTG data is becoming increasingly used in oil and gas exploration. In the fast processing and interpretation of large-scale high-precision data, the use of the graphics processing unit process unit （GPU） and preconditioning methods are very important in the data inversion. In this paper, an improved preconditioned conjugate gradient algorithm is proposed by combining the symmetric successive over-relaxation （SSOR） technique and the incomplete Choleksy decomposition conjugate gradient algorithm （ICCG）. Since preparing the preconditioner requires extra time, a parallel implement based on GPU is proposed. The improved method is then applied in the inversion of noise- contaminated synthetic data to prove its adaptability in the inversion of 3D FTG data. Results show that the parallel SSOR-ICCG algorithm based on NVIDIA Tesla C2050 GPU achieves a speedup of approximately 25 times that of a serial program using a 2.0 GHz Central Processing Unit （CPU）. Real airbome gravity-gradiometry data from Vinton salt dome （south- west Louisiana, USA） are also considered. Good results are obtained, which verifies the efficiency and feasibility of the proposed parallel method in fast inversion of 3D FTG data.
基金supported in part by the National Key Research and Development Program of China(2018AAA0100100)the National Natural Science Foundation of China(61906001,62136008,U21A20512)+1 种基金the Key Program of Natural Science Project of Educational Commission of Anhui Province(KJ2020A0036)Alexander von Humboldt Professorship for Artificial Intelligence Funded by the Federal Ministry of Education and Research,Germany。
文摘Large-scale multi-objective optimization problems(LSMOPs)pose challenges to existing optimizers since a set of well-converged and diverse solutions should be found in huge search spaces.While evolutionary algorithms are good at solving small-scale multi-objective optimization problems,they are criticized for low efficiency in converging to the optimums of LSMOPs.By contrast,mathematical programming methods offer fast convergence speed on large-scale single-objective optimization problems,but they have difficulties in finding diverse solutions for LSMOPs.Currently,how to integrate evolutionary algorithms with mathematical programming methods to solve LSMOPs remains unexplored.In this paper,a hybrid algorithm is tailored for LSMOPs by coupling differential evolution and a conjugate gradient method.On the one hand,conjugate gradients and differential evolution are used to update different decision variables of a set of solutions,where the former drives the solutions to quickly converge towards the Pareto front and the latter promotes the diversity of the solutions to cover the whole Pareto front.On the other hand,objective decomposition strategy of evolutionary multi-objective optimization is used to differentiate the conjugate gradients of solutions,and the line search strategy of mathematical programming is used to ensure the higher quality of each offspring than its parent.In comparison with state-of-the-art evolutionary algorithms,mathematical programming methods,and hybrid algorithms,the proposed algorithm exhibits better convergence and diversity performance on a variety of benchmark and real-world LSMOPs.
基金supported by the National Natural Science Foundation of China (Nos. 40774029, 41004028)the Special Fund for Basic Scientific Research of Central Colleges (No. 2010ZY53)the Program for New Century Excellent Talents in University (NCET)
文摘We developed a three-dimensional（3D） conjugate gradient inversion algorithm for in-verting magnetotelluric impedance tensor measurements.In order to show the importance of including diagonal components of magnetotelluric impedance tensor in 3D inversion,synthetic data were inverted using the 3D conjugate gradient inversion,and the inversion results were compared and analyzed.The results from the 3D inversion of synthetic data indicate that both the off-diagonal and the diagonal components are required in inversions to obtain better inversion results when there are no enough data sites to recover the target resistivity structure.These examples show that lots of information about 3D structure is also contained in the diagonal components;as a result,diagonal components should be in-cluded in 3D inversions.The inversion algorithm was also used to invert the impedance tensor data ac-quired in the Kayabe area in Japan.Inversions with the synthetic and real data demonstrated the va-lidity and practicability of the inversion algorithm.
基金partially supported by the National Natural Science Foundation of China (No.41230318)
文摘With the development of computational power, there has been an increased focus on data-fitting related seismic inversion techniques for high fidelity seismic velocity model and image, such as full-waveform inversion and least squares migration. However, though more advanced than conventional methods, these data fitting methods can be very expensive in terms of computational cost. Recently, various techniques to optimize these data-fitting seismic inversion problems have been implemented to cater for the industrial need for much improved efficiency. In this study, we propose a general stochastic conjugate gradient method for these data-fitting related inverse problems. We first prescribe the basic theory of our method and then give synthetic examples. Our numerical experiments illustrate the potential of this method for large-size seismic inversion application.
基金Supported by Research Council of Semnan University
文摘A hybridization of the three–term conjugate gradient method proposed by Zhang et al. and the nonlinear conjugate gradient method proposed by Polak and Ribi`ere, and Polyak is suggested. Based on an eigenvalue analysis, it is shown that search directions of the proposed method satisfy the sufficient descent condition, independent of the line search and the objective function convexity. Global convergence of the method is established under an Armijo–type line search condition. Numerical experiments show practical efficiency of the proposed method.
基金Supported by the Fund of Chongqing Education Committee(KJ091104)
文摘In this paper,an efficient conjugate gradient method is given to solve the general unconstrained optimization problems,which can guarantee the sufficient descent property and the global convergence with the strong Wolfe line search conditions.Numerical results show that the new method is efficient and stationary by comparing with PRP＋ method,so it can be widely used in scientific computation.
文摘Conjugate gradient optimization algorithms depend on the search directions with different choices for the parameters in the search directions. In this note, by combining the nice numerical performance of PR and HS methods with the global convergence property of the class of conjugate gradient methods presented by HU and STOREY(1991), a class of new restarting conjugate gradient methods is presented. Global convergences of the new method with two kinds of common line searches, are proved. Firstly, it is shown that, using reverse modulus of continuity function and forcing function, the new method for solving unconstrained optimization can work for a continously dif ferentiable function with Curry-Altman's step size rule and a bounded level set. Secondly, by using comparing technique, some general convergence properties of the new method with other kind of step size rule are established. Numerical experiments show that the new method is efficient by comparing with FR conjugate gradient method.
基金Supported by the National Natural Science Foundation of China（10571106） Supported by the Fundamental Research Funds for the Central Universities（10CX04044A）
文摘In this note,by combining the nice numerical performance of PR and HS methods with the global convergence property of FR method,a class of new restarting three terms conjugate gradient methods is presented.Global convergence properties of the new method with two kinds of common line searches are proved.
基金Sponsored by the National Natural Science Foundation of China(Grant No.11901561).
文摘Many methods have been put forward to solve unconstrained optimization problems,among which conjugate gradient method(CG)is very important.With the increasing emergence of large⁃scale problems,the subspace technology has become particularly important and widely used in the field of optimization.In this study,a new CG method was put forward,which combined subspace technology and a cubic regularization model.Besides,a special scaled norm in a cubic regularization model was analyzed.Under certain conditions,some significant characteristics of the search direction were given and the convergence of the algorithm was built.Numerical comparisons show that for the 145 test functions under the CUTEr library,the proposed method is better than two classical CG methods and two new subspaces conjugate gradient methods.
基金Supported by the National Science Foundation of China(10171055)
文摘In [3] Liu et al. investigated global convergence of conjugate gradient methods. In that paper they allowed βκ to be selected in a wider range and the global convergence of the corresponding algorithm without sufficient decrease condition was proved. This paper investigates global convergence of nonmonotone conjugate gradient method under the same conditions.
文摘Nonlinear conjugate gradient methods have played an important role in solving large scale unconstrained optimi-zation problems,it is characterized by the simplicity of their iteration and their low memory requirements.It is well-known that the direction generated by a conjugate gradient method may be not a descent direction.In this paper,a new class of nonlinear conjugate gradient method is presented,its search direction is a descent direction for the objective function.If the objective function is differentiable and its gradient is Lipschitz continuous,the line sbarch satisfies strong Wolfe condition,the global convergence result is established.
