The main purpose of this paper is to use the Chelyshkov-collocation spectral method for solving nonlinear Quadratic integral equations of Volterra type.The method is based on the approximate solutions in terms of Chel...The main purpose of this paper is to use the Chelyshkov-collocation spectral method for solving nonlinear Quadratic integral equations of Volterra type.The method is based on the approximate solutions in terms of Chelyshkov polynomials with unknown coefficients.The Chelyshkov polynomials and their properties are employed to derive the operational matrices of integral and product.The application of these operational matrices for solving the mentioned problem is explained.The error analysis of the proposed method is investigated.Finally,some numerical examples are provided to demonstrate the efficiency of the method.展开更多
The objective of the paper is to develop a new algorithm for numerical solution of dynamic elastic-plastic strain hardening/softening problems. The gradient dependent model is adopted in the numerical model to overcom...The objective of the paper is to develop a new algorithm for numerical solution of dynamic elastic-plastic strain hardening/softening problems. The gradient dependent model is adopted in the numerical model to overcome the result mesh-sensitivity problem in the dynamic strain softening or strain localization analysis. The equations for the dynamic elastic-plastic problems are derived in terms of the parametric variational principle, which is valid for associated, non-associated and strain softening plastic constitutive models in the finite element analysis. The precise integration method, which has been widely used for discretization in time domain of the linear problems, is introduced for the solution of dynamic nonlinear equations. The new algorithm proposed is based on the combination of the parametric quadratic programming method and the precise integration method and has all the advantages in both of the algorithms. Results of numerical examples demonstrate not only the validity, but also the advantages of the algorithm proposed for the numerical solution of nonlinear dynamic problems.展开更多
In this study, forced nonlinear vibration of a circular micro-plate under two-sided electrostatic, two-sided Casimir and external harmonic forces is investigated analytically. For this purpose, at first, von Karman pl...In this study, forced nonlinear vibration of a circular micro-plate under two-sided electrostatic, two-sided Casimir and external harmonic forces is investigated analytically. For this purpose, at first, von Karman plate theory including geometrical nonlinearity is used to obtain the deflection of the micro-plate. Galerkin decomposition method is then employed, and nonlinear ordinary differential equations (ODEs) of motion are determined. A harmonic balance method (HBM) is applied to equations and analytical relation for nonlineaT frequency response (F-R) curves are derived for two categories (including and neglecting Casimir force) separately. The analytical results for three cases:(1) semi-linear vibration;(2) weakly nonlinear vibration;(3) highly non linear vibration, are validated by comparing with the numerical solutio ns. After validation, the effects of the voltage and Casimir force on the natural frequency of two-sided capacitor system are investigated. It is shown that by assuming Casimir force in small gap distances, reduction of the natural frequency is considerable. The influences of the applied voltage, damping, micro-plate thickness and Casimir force on the frequency response curves have been presented too. The results of this study can be useful for modeling circular parallel-plates in nano /microelectromechanical transducers such as microphones and pressure sensors.展开更多
In this study, a multivariate local quadratic polynomial regression(MLQPR) method is proposed to design a model for the sludge volume index(SVI). In MLQPR, a quadratic polynomial regression function is established to ...In this study, a multivariate local quadratic polynomial regression(MLQPR) method is proposed to design a model for the sludge volume index(SVI). In MLQPR, a quadratic polynomial regression function is established to describe the relationship between SVI and the relative variables, and the important terms of the quadratic polynomial regression function are determined by the significant test of the corresponding coefficients. Moreover, a local estimation method is introduced to adjust the weights of the quadratic polynomial regression function to improve the model accuracy. Finally, the proposed method is applied to predict the SVI values in a real wastewater treatment process(WWTP). The experimental results demonstrate that the proposed MLQPR method has faster testing speed and more accurate results than some existing methods.展开更多
Many effective optimization algorithms require partial derivatives of objective functions,while some optimization problems'objective functions have no derivatives.According to former research studies,some search d...Many effective optimization algorithms require partial derivatives of objective functions,while some optimization problems'objective functions have no derivatives.According to former research studies,some search directions are obtained using the quadratic hypothesis of objective functions.Based on derivatives,quadratic function assumptions,and directional derivatives,the computational formulas of numerical first-order partial derivatives,second-order partial derivatives,and numerical second-order mixed partial derivatives were constructed.Based on the coordinate transformation relation,a set of orthogonal vectors in the fixed coordinate system was established according to the optimization direction.A numerical algorithm was proposed,taking the second order approximation direction as an example.A large stepsize numerical algorithm based on coordinate transformation was proposed.Several algorithms were validated by an unconstrained optimization of the two-dimensional Rosenbrock objective function.The numerical second order approximation direction with the numerical mixed partial derivatives showed good results.Its calculated amount is 0.2843%of that of without second-order mixed partial derivative.In the process of rotating the local coordinate system 360°,because the objective function is more complex than the quadratic function,if the numerical direction derivative is used instead of the analytic partial derivative,the optimization direction varies with a range of 103.05°.Because theoretical error is in the numerical negative gradient direction,the calculation with the coordinate transformation is 94.71%less than the calculation without coordinate transformation.If there is no theoretical error in the numerical negative gradient direction or in the large-stepsize numerical optimization algorithm based on the coordinate transformation,the sawtooth phenomenon occurs.When each numerical mixed partial derivative takes more than one point,the optimization results cannot be improved.The numerical direction based on the quadratic hypothesis only requires the objective function to be obtained,but does not require derivability and does not take into account truncation error and rounding error.Thus,the application scopes of many optimization methods are extended.展开更多
A new algorithm for the solution of quadratic programming problemsis put forward in terms of the mixed energy theory and is furtherused for the incremental solution of elastic-plastic trussstructures. The method propo...A new algorithm for the solution of quadratic programming problemsis put forward in terms of the mixed energy theory and is furtherused for the incremental solution of elastic-plastic trussstructures. The method proposed is different from the traditionalone, for which the unknown variables are selected just in one classsuch as displacements or stresses. The present method selects thevariables in the mixed form with both displacement and stress. As themethod is established in the hybrid space, the information found inthe previous incremental step can be used for the solution of thepresent step, making the algorithm highly effi- cient in thenumerical solution process of quadratic programming problems. Theresults obtained in the exm- ples of the elastic-plastic solution ofthe truss structures verify what has been predicted in thetheoretical anal- ysis.展开更多
A noninterior continuation method is proposed for semidefinite complementarity problem （SDCP）. This method improves the noninterior continuation methods recently developed for SDCP by Chen and Tseng. The main proper...A noninterior continuation method is proposed for semidefinite complementarity problem （SDCP）. This method improves the noninterior continuation methods recently developed for SDCP by Chen and Tseng. The main properties of our method are： （i） it is well d.efined for the monotones SDCP; （ii） it has to solve just one linear system of equations at each step; （iii） it is shown to be both globally linearly convergent and locally quadratically convergent under suitable assumptions.展开更多
The high-speed development of space defense technology demands a high state estimation capacity for spacecraft tracking methods.However,reentry flight is accompanied by complex flight environments,which brings to the ...The high-speed development of space defense technology demands a high state estimation capacity for spacecraft tracking methods.However,reentry flight is accompanied by complex flight environments,which brings to the uncertain,complex,and strongly coupled non-Gaussian detection noise.As a result,there are several intractable considerations on the problem of state estimation tasks corrupted by complex non-Gaussian outliers for non-linear dynamics systems in practical application.To address these issues,a new iterated rational quadratic(RQ)kernel high-order unscented Kalman filtering(IRQHUKF)algorithm via capturing the statistics to break through the limitations of the Gaussian assumption is proposed.Firstly,the characteristic analysis of the RQ kernel is investigated in detail,which is the first attempt to carry out an exploration of the heavy-tailed characteristic and the ability on capturing highorder moments of the RQ kernel.Subsequently,the RQ kernel method is first introduced into the UKF algorithm as an error optimization criterion,termed the iterated RQ kernel-UKF(RQ-UKF)algorithm by derived analytically,which not only retains the high-order moments propagation process but also enhances the approximation capacity in the non-Gaussian noise problem for its ability in capturing highorder moments and heavy-tailed characteristics.Meanwhile,to tackle the limitations of the Gaussian distribution assumption in the linearization process of the non-linear systems,the high-order Sigma Points(SP)as a subsidiary role in propagating the state high-order statistics is devised by the moments matching method to improve the RQ-UKF.Finally,to further improve the flexibility of the IRQ-HUKF algorithm in practical application,an adaptive kernel parameter is derived analytically grounded in the Kullback-Leibler divergence(KLD)method and parametric sensitivity analysis of the RQ kernel.The simulation results demonstrate that the novel IRQ-HUKF algorithm is more robust and outperforms the existing advanced UKF with respect to the kernel method in reentry vehicle tracking scenarios under various noise environments.展开更多
In this paper,two-stage stochastic quadratic programming problems with equality constraints are considered.By Monte Carlo simulation-based approximations of the objective function and its first(second)derivative,an in...In this paper,two-stage stochastic quadratic programming problems with equality constraints are considered.By Monte Carlo simulation-based approximations of the objective function and its first(second)derivative,an inexact Lagrange-Newton type method is proposed.It is showed that this method is globally convergent with probability one.In particular,the convergence is local superlinear under an integral approximation error bound condition.Moreover,this method can be easily extended to solve stochastic quadratic programming problems with inequality constraints.展开更多
A one_step smoothing Newton method is proposed for solving the vertical linear complementarity problem based on the so_called aggregation function. The proposed algorithm has the following good features: (ⅰ) It solve...A one_step smoothing Newton method is proposed for solving the vertical linear complementarity problem based on the so_called aggregation function. The proposed algorithm has the following good features: (ⅰ) It solves only one linear system of equations and does only one line search at each iteration; (ⅱ) It is well_defined for the vertical linear complementarity problem with vertical block P 0 matrix and any accumulation point of iteration sequence is its solution.Moreover, the iteration sequence is bounded for the vertical linear complementarity problem with vertical block P 0+R 0 matrix; (ⅲ) It has both global linear and local quadratic convergence without strict complementarity. Many existing smoothing Newton methods do not have the property (ⅲ).展开更多
In this article, we compute the enclosures eigenvalues (upper and lower bounds) using the quadratic method. The Schrodinger operator (A) (harmonic and anharmonic oscillator model) has used as an example. We study a ne...In this article, we compute the enclosures eigenvalues (upper and lower bounds) using the quadratic method. The Schrodinger operator (A) (harmonic and anharmonic oscillator model) has used as an example. We study a new technique to get more accurate bounds. We compare our results with Boulton and Strauss method.展开更多
This paper discusses the two-block large-scale nonconvex optimization problem with general linear constraints.Based on the ideas of splitting and sequential quadratic optimization(SQO),a new feasible descent method fo...This paper discusses the two-block large-scale nonconvex optimization problem with general linear constraints.Based on the ideas of splitting and sequential quadratic optimization(SQO),a new feasible descent method for the discussed problem is proposed.First,we consider the problem of quadratic optimal(QO)approximation associated with the current feasible iteration point,and we split the QO into two small-scale QOs which can be solved in parallel.Second,a feasible descent direction for the problem is obtained and a new SQO-type method is proposed,namely,splitting feasible SQO(SF-SQO)method.Moreover,under suitable conditions,we analyse the global convergence,strong convergence and rate of superlinear convergence of the SF-SQO method.Finally,preliminary numerical experiments regarding the economic dispatch of a power system are carried out,and these show that the SF-SQO method is promising.展开更多
In this paper we present a new method for solving the Stokes problem which is a constrained optimization method. The new method is simpler and requires less computation than the existing methods. In this method we tra...In this paper we present a new method for solving the Stokes problem which is a constrained optimization method. The new method is simpler and requires less computation than the existing methods. In this method we transform the Stokes problem into a quadratic programming problem and by solving it, the velocity and the pressure are obtained.展开更多
Quadratic matrix equations arise in many elds of scienti c computing and engineering applications.In this paper,we consider a class of quadratic matrix equations.Under a certain condition,we rst prove the existence of...Quadratic matrix equations arise in many elds of scienti c computing and engineering applications.In this paper,we consider a class of quadratic matrix equations.Under a certain condition,we rst prove the existence of minimal nonnegative solution for this quadratic matrix equation,and then propose some numerical methods for solving it.Convergence analysis and numerical examples are given to verify the theories and the numerical methods of this paper.展开更多
In this paper, we apply the modified Adomian Decomposition Method to get the numerical solutions of Quadratic integral equations. The appearance of noise terms in Decomposition Method was investigated. The method was ...In this paper, we apply the modified Adomian Decomposition Method to get the numerical solutions of Quadratic integral equations. The appearance of noise terms in Decomposition Method was investigated. The method was described along with several examples.展开更多
The paper presents an approach for avoiding and minimizing the complementary pivots in a simplex based solution method for a quadratic programming problem. The linearization of the problem is slightly changed so that ...The paper presents an approach for avoiding and minimizing the complementary pivots in a simplex based solution method for a quadratic programming problem. The linearization of the problem is slightly changed so that the simplex or interior point methods can solve with full speed. This is a big advantage as a complementary pivot algorithm will take roughly eight times as longer time to solve a quadratic program than the full speed simplex-method solving a linear problem of the same size. The strategy of the approach is in the assumption that the solution of the quadratic programming problem is near the feasible point closest to the stationary point assuming no constraints.展开更多
In this paper, a modified version of the Classical Lagrange Multiplier method is developed for convex quadratic optimization problems. The method, which is evolved from the first order derivative test for optimality o...In this paper, a modified version of the Classical Lagrange Multiplier method is developed for convex quadratic optimization problems. The method, which is evolved from the first order derivative test for optimality of the Lagrangian function with respect to the primary variables of the problem, decomposes the solution process into two independent ones, in which the primary variables are solved for independently, and then the secondary variables, which are the Lagrange multipliers, are solved for, afterward. This is an innovation that leads to solving independently two simpler systems of equations involving the primary variables only, on one hand, and the secondary ones on the other. Solutions obtained for small sized problems (as preliminary test of the method) demonstrate that the new method is generally effective in producing the required solutions.展开更多
In this paper, a new primal-dual interior-point algorithm for convex quadratic optimization （CQO） based on a kernel function is presented. The proposed function has some properties that are easy for checking. These ...In this paper, a new primal-dual interior-point algorithm for convex quadratic optimization （CQO） based on a kernel function is presented. The proposed function has some properties that are easy for checking. These properties enable us to improve the polynomial complexity bound of a large-update interior-point method （IPM） to O（√n log nlog n/e）, which is the currently best known polynomial complexity bound for the algorithm with the large-update method. Numerical tests were conducted to investigate the behavior of the algorithm with different parameters p, q and θ, where p is the growth degree parameter, q is the barrier degree of the kernel function and θ is the barrier update parameter.展开更多
Using the fixed point method, this article proves the Hyers-Ulam-Rassias stability of a generalized Apollonius type quadratic functional equation in Banach spaces. The conditions of these results are demonstrated by t...Using the fixed point method, this article proves the Hyers-Ulam-Rassias stability of a generalized Apollonius type quadratic functional equation in Banach spaces. The conditions of these results are demonstrated by the quadratic functional equation of Apollonius type.展开更多
文摘The main purpose of this paper is to use the Chelyshkov-collocation spectral method for solving nonlinear Quadratic integral equations of Volterra type.The method is based on the approximate solutions in terms of Chelyshkov polynomials with unknown coefficients.The Chelyshkov polynomials and their properties are employed to derive the operational matrices of integral and product.The application of these operational matrices for solving the mentioned problem is explained.The error analysis of the proposed method is investigated.Finally,some numerical examples are provided to demonstrate the efficiency of the method.
文摘The objective of the paper is to develop a new algorithm for numerical solution of dynamic elastic-plastic strain hardening/softening problems. The gradient dependent model is adopted in the numerical model to overcome the result mesh-sensitivity problem in the dynamic strain softening or strain localization analysis. The equations for the dynamic elastic-plastic problems are derived in terms of the parametric variational principle, which is valid for associated, non-associated and strain softening plastic constitutive models in the finite element analysis. The precise integration method, which has been widely used for discretization in time domain of the linear problems, is introduced for the solution of dynamic nonlinear equations. The new algorithm proposed is based on the combination of the parametric quadratic programming method and the precise integration method and has all the advantages in both of the algorithms. Results of numerical examples demonstrate not only the validity, but also the advantages of the algorithm proposed for the numerical solution of nonlinear dynamic problems.
文摘In this study, forced nonlinear vibration of a circular micro-plate under two-sided electrostatic, two-sided Casimir and external harmonic forces is investigated analytically. For this purpose, at first, von Karman plate theory including geometrical nonlinearity is used to obtain the deflection of the micro-plate. Galerkin decomposition method is then employed, and nonlinear ordinary differential equations (ODEs) of motion are determined. A harmonic balance method (HBM) is applied to equations and analytical relation for nonlineaT frequency response (F-R) curves are derived for two categories (including and neglecting Casimir force) separately. The analytical results for three cases:(1) semi-linear vibration;(2) weakly nonlinear vibration;(3) highly non linear vibration, are validated by comparing with the numerical solutio ns. After validation, the effects of the voltage and Casimir force on the natural frequency of two-sided capacitor system are investigated. It is shown that by assuming Casimir force in small gap distances, reduction of the natural frequency is considerable. The influences of the applied voltage, damping, micro-plate thickness and Casimir force on the frequency response curves have been presented too. The results of this study can be useful for modeling circular parallel-plates in nano /microelectromechanical transducers such as microphones and pressure sensors.
文摘In this study, a multivariate local quadratic polynomial regression(MLQPR) method is proposed to design a model for the sludge volume index(SVI). In MLQPR, a quadratic polynomial regression function is established to describe the relationship between SVI and the relative variables, and the important terms of the quadratic polynomial regression function are determined by the significant test of the corresponding coefficients. Moreover, a local estimation method is introduced to adjust the weights of the quadratic polynomial regression function to improve the model accuracy. Finally, the proposed method is applied to predict the SVI values in a real wastewater treatment process(WWTP). The experimental results demonstrate that the proposed MLQPR method has faster testing speed and more accurate results than some existing methods.
基金supported in part by the Teaching Reform Research Foundation of Shengli College in China University of Petroleum(East China)(JG201725)the Natural Science Foundation Shandong Province of China(ZR2018PEE009)the Project of Science and Technology of Shandong Universities in China(J17KA044,J17KB061)。
文摘Many effective optimization algorithms require partial derivatives of objective functions,while some optimization problems'objective functions have no derivatives.According to former research studies,some search directions are obtained using the quadratic hypothesis of objective functions.Based on derivatives,quadratic function assumptions,and directional derivatives,the computational formulas of numerical first-order partial derivatives,second-order partial derivatives,and numerical second-order mixed partial derivatives were constructed.Based on the coordinate transformation relation,a set of orthogonal vectors in the fixed coordinate system was established according to the optimization direction.A numerical algorithm was proposed,taking the second order approximation direction as an example.A large stepsize numerical algorithm based on coordinate transformation was proposed.Several algorithms were validated by an unconstrained optimization of the two-dimensional Rosenbrock objective function.The numerical second order approximation direction with the numerical mixed partial derivatives showed good results.Its calculated amount is 0.2843%of that of without second-order mixed partial derivative.In the process of rotating the local coordinate system 360°,because the objective function is more complex than the quadratic function,if the numerical direction derivative is used instead of the analytic partial derivative,the optimization direction varies with a range of 103.05°.Because theoretical error is in the numerical negative gradient direction,the calculation with the coordinate transformation is 94.71%less than the calculation without coordinate transformation.If there is no theoretical error in the numerical negative gradient direction or in the large-stepsize numerical optimization algorithm based on the coordinate transformation,the sawtooth phenomenon occurs.When each numerical mixed partial derivative takes more than one point,the optimization results cannot be improved.The numerical direction based on the quadratic hypothesis only requires the objective function to be obtained,but does not require derivability and does not take into account truncation error and rounding error.Thus,the application scopes of many optimization methods are extended.
基金the National Natural Science Foundation of China(No.50178916,No.19732020 and No.19872016)the National Key Basic lteseareh Special Foundation(No.G1999032805)+1 种基金the Special Funds for Major State Basic Researeh Projectsthe Foundation for University Key Teachers by the Ministry of Education of China
文摘A new algorithm for the solution of quadratic programming problemsis put forward in terms of the mixed energy theory and is furtherused for the incremental solution of elastic-plastic trussstructures. The method proposed is different from the traditionalone, for which the unknown variables are selected just in one classsuch as displacements or stresses. The present method selects thevariables in the mixed form with both displacement and stress. As themethod is established in the hybrid space, the information found inthe previous incremental step can be used for the solution of thepresent step, making the algorithm highly effi- cient in thenumerical solution process of quadratic programming problems. Theresults obtained in the exm- ples of the elastic-plastic solution ofthe truss structures verify what has been predicted in thetheoretical anal- ysis.
基金This work was supported by the National Natural Science Foundation of China (10201001, 70471008)
文摘A noninterior continuation method is proposed for semidefinite complementarity problem （SDCP）. This method improves the noninterior continuation methods recently developed for SDCP by Chen and Tseng. The main properties of our method are： （i） it is well d.efined for the monotones SDCP; （ii） it has to solve just one linear system of equations at each step; （iii） it is shown to be both globally linearly convergent and locally quadratically convergent under suitable assumptions.
基金supported by the National Natural Science Foundation of China under Grant No.12072090.
文摘The high-speed development of space defense technology demands a high state estimation capacity for spacecraft tracking methods.However,reentry flight is accompanied by complex flight environments,which brings to the uncertain,complex,and strongly coupled non-Gaussian detection noise.As a result,there are several intractable considerations on the problem of state estimation tasks corrupted by complex non-Gaussian outliers for non-linear dynamics systems in practical application.To address these issues,a new iterated rational quadratic(RQ)kernel high-order unscented Kalman filtering(IRQHUKF)algorithm via capturing the statistics to break through the limitations of the Gaussian assumption is proposed.Firstly,the characteristic analysis of the RQ kernel is investigated in detail,which is the first attempt to carry out an exploration of the heavy-tailed characteristic and the ability on capturing highorder moments of the RQ kernel.Subsequently,the RQ kernel method is first introduced into the UKF algorithm as an error optimization criterion,termed the iterated RQ kernel-UKF(RQ-UKF)algorithm by derived analytically,which not only retains the high-order moments propagation process but also enhances the approximation capacity in the non-Gaussian noise problem for its ability in capturing highorder moments and heavy-tailed characteristics.Meanwhile,to tackle the limitations of the Gaussian distribution assumption in the linearization process of the non-linear systems,the high-order Sigma Points(SP)as a subsidiary role in propagating the state high-order statistics is devised by the moments matching method to improve the RQ-UKF.Finally,to further improve the flexibility of the IRQ-HUKF algorithm in practical application,an adaptive kernel parameter is derived analytically grounded in the Kullback-Leibler divergence(KLD)method and parametric sensitivity analysis of the RQ kernel.The simulation results demonstrate that the novel IRQ-HUKF algorithm is more robust and outperforms the existing advanced UKF with respect to the kernel method in reentry vehicle tracking scenarios under various noise environments.
基金Partly supported by the National Natural Science Foundation of China( 1 0 1 71 0 5 5 )
文摘In this paper,two-stage stochastic quadratic programming problems with equality constraints are considered.By Monte Carlo simulation-based approximations of the objective function and its first(second)derivative,an inexact Lagrange-Newton type method is proposed.It is showed that this method is globally convergent with probability one.In particular,the convergence is local superlinear under an integral approximation error bound condition.Moreover,this method can be easily extended to solve stochastic quadratic programming problems with inequality constraints.
文摘A one_step smoothing Newton method is proposed for solving the vertical linear complementarity problem based on the so_called aggregation function. The proposed algorithm has the following good features: (ⅰ) It solves only one linear system of equations and does only one line search at each iteration; (ⅱ) It is well_defined for the vertical linear complementarity problem with vertical block P 0 matrix and any accumulation point of iteration sequence is its solution.Moreover, the iteration sequence is bounded for the vertical linear complementarity problem with vertical block P 0+R 0 matrix; (ⅲ) It has both global linear and local quadratic convergence without strict complementarity. Many existing smoothing Newton methods do not have the property (ⅲ).
文摘In this article, we compute the enclosures eigenvalues (upper and lower bounds) using the quadratic method. The Schrodinger operator (A) (harmonic and anharmonic oscillator model) has used as an example. We study a new technique to get more accurate bounds. We compare our results with Boulton and Strauss method.
基金supported by the National Natural Science Foundation of China(12171106)the Natural Science Foundation of Guangxi Province(2020GXNSFDA238017 and 2018GXNSFFA281007)the Shanghai Sailing Program(21YF1430300)。
文摘This paper discusses the two-block large-scale nonconvex optimization problem with general linear constraints.Based on the ideas of splitting and sequential quadratic optimization(SQO),a new feasible descent method for the discussed problem is proposed.First,we consider the problem of quadratic optimal(QO)approximation associated with the current feasible iteration point,and we split the QO into two small-scale QOs which can be solved in parallel.Second,a feasible descent direction for the problem is obtained and a new SQO-type method is proposed,namely,splitting feasible SQO(SF-SQO)method.Moreover,under suitable conditions,we analyse the global convergence,strong convergence and rate of superlinear convergence of the SF-SQO method.Finally,preliminary numerical experiments regarding the economic dispatch of a power system are carried out,and these show that the SF-SQO method is promising.
文摘In this paper we present a new method for solving the Stokes problem which is a constrained optimization method. The new method is simpler and requires less computation than the existing methods. In this method we transform the Stokes problem into a quadratic programming problem and by solving it, the velocity and the pressure are obtained.
基金Supported by the National Natural Science Foundation of China(12001395)the special fund for Science and Technology Innovation Teams of Shanxi Province(202204051002018)+1 种基金Research Project Supported by Shanxi Scholarship Council of China(2022-169)Graduate Education Innovation Project of Taiyuan Normal University(SYYJSYC-2314)。
文摘Quadratic matrix equations arise in many elds of scienti c computing and engineering applications.In this paper,we consider a class of quadratic matrix equations.Under a certain condition,we rst prove the existence of minimal nonnegative solution for this quadratic matrix equation,and then propose some numerical methods for solving it.Convergence analysis and numerical examples are given to verify the theories and the numerical methods of this paper.
文摘In this paper, we apply the modified Adomian Decomposition Method to get the numerical solutions of Quadratic integral equations. The appearance of noise terms in Decomposition Method was investigated. The method was described along with several examples.
文摘The paper presents an approach for avoiding and minimizing the complementary pivots in a simplex based solution method for a quadratic programming problem. The linearization of the problem is slightly changed so that the simplex or interior point methods can solve with full speed. This is a big advantage as a complementary pivot algorithm will take roughly eight times as longer time to solve a quadratic program than the full speed simplex-method solving a linear problem of the same size. The strategy of the approach is in the assumption that the solution of the quadratic programming problem is near the feasible point closest to the stationary point assuming no constraints.
文摘In this paper, a modified version of the Classical Lagrange Multiplier method is developed for convex quadratic optimization problems. The method, which is evolved from the first order derivative test for optimality of the Lagrangian function with respect to the primary variables of the problem, decomposes the solution process into two independent ones, in which the primary variables are solved for independently, and then the secondary variables, which are the Lagrange multipliers, are solved for, afterward. This is an innovation that leads to solving independently two simpler systems of equations involving the primary variables only, on one hand, and the secondary ones on the other. Solutions obtained for small sized problems (as preliminary test of the method) demonstrate that the new method is generally effective in producing the required solutions.
基金the Foundation of Scientific Research for Selecting and Cultivating Young Excellent University Teachers in Shanghai (Grant No.06XPYQ52)the Shanghai Pujiang Program (Grant No.06PJ14039)
文摘In this paper, a new primal-dual interior-point algorithm for convex quadratic optimization （CQO） based on a kernel function is presented. The proposed function has some properties that are easy for checking. These properties enable us to improve the polynomial complexity bound of a large-update interior-point method （IPM） to O（√n log nlog n/e）, which is the currently best known polynomial complexity bound for the algorithm with the large-update method. Numerical tests were conducted to investigate the behavior of the algorithm with different parameters p, q and θ, where p is the growth degree parameter, q is the barrier degree of the kernel function and θ is the barrier update parameter.
文摘Using the fixed point method, this article proves the Hyers-Ulam-Rassias stability of a generalized Apollonius type quadratic functional equation in Banach spaces. The conditions of these results are demonstrated by the quadratic functional equation of Apollonius type.
