A class of trust region methods for solving linear inequality constrained problems is proposed in this paper. It is shown that the algorithm is of global convergence.The algorithm uses a version of the two-sided proje...A class of trust region methods for solving linear inequality constrained problems is proposed in this paper. It is shown that the algorithm is of global convergence.The algorithm uses a version of the two-sided projection and the strategy of the unconstrained trust region methods. It keeps the good convergence properties of the unconstrained case and has the merits of the projection method. In some sense, our algorithm can be regarded as an extension and improvement of the projected type algorithm.展开更多
In this paper, a new trust region algorithm for nonlinear equality constrained LC1 optimization problems is given. It obtains a search direction at each iteration not by solving a quadratic programming subprobiem with...In this paper, a new trust region algorithm for nonlinear equality constrained LC1 optimization problems is given. It obtains a search direction at each iteration not by solving a quadratic programming subprobiem with a trust region bound, but by solving a system of linear equations. Since the computational complexity of a QP-Problem is in general much larger than that of a system of linear equations, this method proposed in this paper may reduce the computational complexity and hence improve computational efficiency. Furthermore, it is proved under appropriate assumptions that this algorithm is globally and super-linearly convergent to a solution of the original problem. Some numerical examples are reported, showing the proposed algorithm can be beneficial from a computational point of view.展开更多
In this paper, a new trust region algorithm for unconstrained LC1 optimization problems is given. Compare with those existing trust regiion methods, this algorithm has a different feature: it obtains a stepsize at eac...In this paper, a new trust region algorithm for unconstrained LC1 optimization problems is given. Compare with those existing trust regiion methods, this algorithm has a different feature: it obtains a stepsize at each iteration not by soloving a quadratic subproblem with a trust region bound, but by solving a system of linear equations. Thus it reduces computational complexity and improves computation efficiency. It is proven that this algorithm is globally convergent and locally superlinear under some conditions.展开更多
Surrogate-Based Optimization(SBO) is becoming increasingly popular since it can remarkably reduce the computational cost for design optimizations based on high-fidelity and expensive numerical analyses. However, for c...Surrogate-Based Optimization(SBO) is becoming increasingly popular since it can remarkably reduce the computational cost for design optimizations based on high-fidelity and expensive numerical analyses. However, for complicated optimization problems with a large design space, many design variables, and strong nonlinearity, SBO converges slowly and shows imperfection in local exploitation. This paper proposes a trust region method within the framework of an SBO process based on the Kriging model. In each refinement cycle, new samples are selected by a certain design of experiment method within a variable design space, which is sequentially updated by the trust region method. A multi-dimensional trust-region radius is proposed to improve the adaptability of the developed methodology. Further, the scale factor and the limit factor of the trust region are studied to evaluate their effects on the optimization process. Thereafter, different SBO methods using error-based exploration, prediction-based exploitation, refinement based on the expected improvement function, a hybrid refinement strategy, and the developed trust-regionbased refinement are utilized in four analytical tests. Further, the developed optimization methodology is employed in the drag minimization of an RAE2822 airfoil. Results indicate that it has better robustness and local exploitation capability in comparison with those of other SBO展开更多
A new trust region algorithm for solving convex LC 1 optimization problem is presented.It is proved that the algorithm is globally convergent and the rate of convergence is superlinear under some reasonable assum...A new trust region algorithm for solving convex LC 1 optimization problem is presented.It is proved that the algorithm is globally convergent and the rate of convergence is superlinear under some reasonable assumptions.展开更多
In this paper we present a filter-trust-region algorithm for solving LC1 unconstrained optimization problems which uses the second Dini upper directional derivative. We establish the global convergence of the algorith...In this paper we present a filter-trust-region algorithm for solving LC1 unconstrained optimization problems which uses the second Dini upper directional derivative. We establish the global convergence of the algorithm under reasonable assumptions.展开更多
It is well known that trust region methods are very effective for optimization problems. In this article, a new adaptive trust region method is presented for solving uncon- strained optimization problems. The proposed...It is well known that trust region methods are very effective for optimization problems. In this article, a new adaptive trust region method is presented for solving uncon- strained optimization problems. The proposed method combines a modified secant equation with the BFGS updated formula and an adaptive trust region radius, where the new trust region radius makes use of not only the function information but also the gradient information. Under suitable conditions, global convergence is proved, and we demonstrate the local superlinear convergence of the proposed method. The numerical results indicate that the proposed method is very efficient.展开更多
A trust region algorithm for equality constrained optimization is given in this paper.The algorithm does not enforce strict monotonicity of the merit function for every iteration.Global convergence of the algorithm i...A trust region algorithm for equality constrained optimization is given in this paper.The algorithm does not enforce strict monotonicity of the merit function for every iteration.Global convergence of the algorithm is proved under the same conditions of usual trust region method.展开更多
Trust region methods are powerful and effective optimization methods. The conic model method is a new type of method with more information available at each iteration than standard quadratic-based methods. The adva...Trust region methods are powerful and effective optimization methods. The conic model method is a new type of method with more information available at each iteration than standard quadratic-based methods. The advantages of the above two methods can be combined to form a more powerful method for constrained optimization. The trust region subproblem of our method is to minimize a conic function subject to the linearized constraints and trust region bound. At the same time, the new algorithm still possesses robust global properties. The global convergence of the new algorithm under standard conditions is established.展开更多
In this paper, we propose a retrospective filter trust region algorithm for unconstrained optimization, which is based on the framework of the retrospective trust region method and associated with the technique of the...In this paper, we propose a retrospective filter trust region algorithm for unconstrained optimization, which is based on the framework of the retrospective trust region method and associated with the technique of the multi-dimensional filter. The new algorithm gives a good estimation of trust region radius, relaxes the condition of accepting a trial step for the usual trust region methods. Under reasonable assumptions, we analyze the global convergence of the new method and report the preliminary results of numerical tests. We compare the results with those of the basic trust region algorithm, the filter trust region algorithm and the retrospective trust region algorithm, which shows the effectiveness of the new algorithm.展开更多
In this paper, we propose and analyze a non-monotone trust region method with non-monotone line search strategy for unconstrained optimization problems. Unlike the traditional non-monotone trust region method, our alg...In this paper, we propose and analyze a non-monotone trust region method with non-monotone line search strategy for unconstrained optimization problems. Unlike the traditional non-monotone trust region method, our algorithm utilizes non-monotone Wolfe line search to get the next point if a trial step is not adopted. Thus, it can reduce the number of solving sub-problems. Theoretical analysis shows that the new proposed method has a global convergence under some mild conditions.展开更多
This paper presents a new trust region algorithm for solving a class of composite nonsmooth optimizations. It is distinguished by the fact that this method does not enforce strict monotonicity of the objective functio...This paper presents a new trust region algorithm for solving a class of composite nonsmooth optimizations. It is distinguished by the fact that this method does not enforce strict monotonicity of the objective function values at successive iterates and that this method extends the existing results for this type of nonlinear optimization with smooth, or piecewise smooth, or convex objective functions or their composition. It is proved that this algorithm is globally convergent under certain conditions. Finally, some numerical results for several optimization problems are reported which show that the nonmonotonic trust region method is competitive with the usual trust region method.展开更多
This paper presents a trust region two phase model algorithm for solving the equality and bound constrained nonlinear optimization problem. A concept of substationary point is given. Under suitable assumptions,the gl...This paper presents a trust region two phase model algorithm for solving the equality and bound constrained nonlinear optimization problem. A concept of substationary point is given. Under suitable assumptions,the global convergence of this algorithm is proved without assuming the linear independence of the gradient of active constraints. A numerical example is also presented.展开更多
To overcome the shortcomings of the traditional artificial potential field method in mobile robot path planning, an improved artificial potential field model （IAPFM） was established, then a new path planning method ...To overcome the shortcomings of the traditional artificial potential field method in mobile robot path planning, an improved artificial potential field model （IAPFM） was established, then a new path planning method combining the IAPFM with optimization algorithm （trust region algorithm） is proposed. Attractive force between the robot and the target location, and repulsive force between the robot and the obstacles are both converted to the potential field intensity; and filled potential field is used to guide the robot to go out of the local minimum points ; on this basis, the effect of dynamic obstacles velocity and the robot＇s velocity is consid thers and the IAPFM is established, then both the expressions of the attractive potential field and the repulsive potential field are obtained. The trust region algorithm is used to search the minimum value of the sum of all the potential field inten- sities within the movement scope which the robot can arrive in a sampling period. Connecting of all the points which hare the minimum intensity in every sampling period constitutes the global optimization path. Experiment result shows that the method can meet the real-time requirement, and is able to execute the mobile robot path planning task effectively in the dynamic environment.展开更多
In this paper, a new derivative free trust region method is developed based on the conic interpolation model for the unconstrained optimization. The conic interpolation model is built by means of the quadratic model f...In this paper, a new derivative free trust region method is developed based on the conic interpolation model for the unconstrained optimization. The conic interpolation model is built by means of the quadratic model function, the collinear scaling formula, quadratic approximation and interpolation. All the parameters in this model are determined by objective function interpolation condition. A new derivative free method is developed based upon this model and the global convergence of this new method is proved without any information on gradient.展开更多
In this paper, we present a new line search and trust region algorithm for unconstrained optimization problems. The trust region center locates at somewhere in the negative gradient direction with the current best ite...In this paper, we present a new line search and trust region algorithm for unconstrained optimization problems. The trust region center locates at somewhere in the negative gradient direction with the current best iterative point being on the boundary. By doing these, the trust region subproblems are constructed at a new way different with the traditional ones. Then, we test the efficiency of the new line search and trust region algorithm on some standard benchmarking. The computational results reveal that, for most test problems, the number of function and gradient calculations are reduced significantly.展开更多
The trust region method plays an important role in solving optimization problems. In this paper, we propose a new nonmonotone adaptive trust region method for solving unconstrained optimization problems. Actually, we ...The trust region method plays an important role in solving optimization problems. In this paper, we propose a new nonmonotone adaptive trust region method for solving unconstrained optimization problems. Actually, we combine a popular nonmonotone technique with an adaptive trust region algorithm. The new ratio to adjusting the next trust region radius is different from the ratio in the traditional trust region methods. Under some appropriate conditions, we show that the new algorithm has good global convergence and superlinear convergence.展开更多
The secant methods discussed by Fontecilla (in 1988) are considerably revised through employing a trust region multiplier strategy and introducing a nondifferentiable merit function. In this paper the secant methods a...The secant methods discussed by Fontecilla (in 1988) are considerably revised through employing a trust region multiplier strategy and introducing a nondifferentiable merit function. In this paper the secant methods are also improved by adding a dogleg typed movement which allows to overcome a phenomena similar to the Maratos effect. Furthermore, these algorithms are analyzed and global convergence theorems as well as local superlinear convergence rate are proved.展开更多
In this paper, we present a regularized Newton method (M-RNM) with correction for minimizing a convex function whose Hessian matrices may be singular. At every iteration, not only a RNM step is computed but also two c...In this paper, we present a regularized Newton method (M-RNM) with correction for minimizing a convex function whose Hessian matrices may be singular. At every iteration, not only a RNM step is computed but also two correction steps are computed. We show that if the objective function is LC<sup>2</sup>, then the method posses globally convergent. Numerical results show that the new algorithm performs very well.展开更多
The film-covered sweet potato transplanting method requires ensuring the transplantation conditions of small planting holes and large lateral displacement.In the soil insertion phase,the transplantation machine requir...The film-covered sweet potato transplanting method requires ensuring the transplantation conditions of small planting holes and large lateral displacement.In the soil insertion phase,the transplantation machine requires a mechanism design with multiple timed poses,and the existing design methods are still imperfect.For this reason,this article proposes a multi-target trust region parameter-guided optimization algorithm.This algorithm aims to achieve multi-objective optimization design with more timed pose conditions starting from individual timed pose conditions.First,multi-target problems are decomposed into multiple subproblems,and the parameter arrays are kept with the minimum polymerization value of each subproblem.Then,the approximate function value reduction for each target is calculated using this parameter set,and the step size for the next iteration of each subproblem is determined by comparing this approximate reduction with the actual reduction.After many iteration calculations,the parameter arrays end the calculation when the parameter group is no longer updated.This paper uses the design of a film-covered sweet potato transplanting mechanism as a complex optimized application example.The algorithm is used to obtain the optimization results of the target values of eight groups of institutions.The smallest hole is 2.99 mm,and the horizontal transplanting distance is 108.40 mm.The maximum hole is 17.64 mm,and the horizontal transplanting distance is 124.97 mm.Considering the size of the hole and the horizontal transplanting distance of sweet potato transplanting,the mechanism’s target value of the horizontal transplanting distance at 119.92 mm and the hole size at 0.31 mm were selected to design the sweet potato transplanting machine.The correctness of the results is verified,which reflects the practicability of the algorithm.展开更多
文摘A class of trust region methods for solving linear inequality constrained problems is proposed in this paper. It is shown that the algorithm is of global convergence.The algorithm uses a version of the two-sided projection and the strategy of the unconstrained trust region methods. It keeps the good convergence properties of the unconstrained case and has the merits of the projection method. In some sense, our algorithm can be regarded as an extension and improvement of the projected type algorithm.
文摘In this paper, a new trust region algorithm for nonlinear equality constrained LC1 optimization problems is given. It obtains a search direction at each iteration not by solving a quadratic programming subprobiem with a trust region bound, but by solving a system of linear equations. Since the computational complexity of a QP-Problem is in general much larger than that of a system of linear equations, this method proposed in this paper may reduce the computational complexity and hence improve computational efficiency. Furthermore, it is proved under appropriate assumptions that this algorithm is globally and super-linearly convergent to a solution of the original problem. Some numerical examples are reported, showing the proposed algorithm can be beneficial from a computational point of view.
文摘In this paper, a new trust region algorithm for unconstrained LC1 optimization problems is given. Compare with those existing trust regiion methods, this algorithm has a different feature: it obtains a stepsize at each iteration not by soloving a quadratic subproblem with a trust region bound, but by solving a system of linear equations. Thus it reduces computational complexity and improves computation efficiency. It is proven that this algorithm is globally convergent and locally superlinear under some conditions.
基金co-supported by the National Natural Science Foundation of China (No. 11502209)the Free Research Projects of the Central University Funding of China (No. 3102015ZY007)
文摘Surrogate-Based Optimization(SBO) is becoming increasingly popular since it can remarkably reduce the computational cost for design optimizations based on high-fidelity and expensive numerical analyses. However, for complicated optimization problems with a large design space, many design variables, and strong nonlinearity, SBO converges slowly and shows imperfection in local exploitation. This paper proposes a trust region method within the framework of an SBO process based on the Kriging model. In each refinement cycle, new samples are selected by a certain design of experiment method within a variable design space, which is sequentially updated by the trust region method. A multi-dimensional trust-region radius is proposed to improve the adaptability of the developed methodology. Further, the scale factor and the limit factor of the trust region are studied to evaluate their effects on the optimization process. Thereafter, different SBO methods using error-based exploration, prediction-based exploitation, refinement based on the expected improvement function, a hybrid refinement strategy, and the developed trust-regionbased refinement are utilized in four analytical tests. Further, the developed optimization methodology is employed in the drag minimization of an RAE2822 airfoil. Results indicate that it has better robustness and local exploitation capability in comparison with those of other SBO
基金Supported by the National Natural Science Foundation of P.R.China(1 9971 0 0 2 ) and the Subject ofBeijing Educational Committ
文摘A new trust region algorithm for solving convex LC 1 optimization problem is presented.It is proved that the algorithm is globally convergent and the rate of convergence is superlinear under some reasonable assumptions.
基金Supported by CERG: CityU 101005 of the Government of Hong Kong SAR, Chinathe National Natural ScienceFoundation of China, the Specialized Research Fund of Doctoral Program of Higher Education of China (Grant No.20040319003)the Natural Science Fund of Jiangsu Province of China (Grant No. BK2006214)
文摘In this paper we present a filter-trust-region algorithm for solving LC1 unconstrained optimization problems which uses the second Dini upper directional derivative. We establish the global convergence of the algorithm under reasonable assumptions.
基金Supported by the National Natural Science Foundation of China(11661009)the Guangxi Science Fund for Distinguished Young Scholars(2015GXNSFGA139001)+1 种基金the Guangxi Natural Science Key Fund(2017GXNSFDA198046)the Basic Ability Promotion Project of Guangxi Young and Middle-Aged Teachers(2017KY0019)
文摘It is well known that trust region methods are very effective for optimization problems. In this article, a new adaptive trust region method is presented for solving uncon- strained optimization problems. The proposed method combines a modified secant equation with the BFGS updated formula and an adaptive trust region radius, where the new trust region radius makes use of not only the function information but also the gradient information. Under suitable conditions, global convergence is proved, and we demonstrate the local superlinear convergence of the proposed method. The numerical results indicate that the proposed method is very efficient.
文摘A trust region algorithm for equality constrained optimization is given in this paper.The algorithm does not enforce strict monotonicity of the merit function for every iteration.Global convergence of the algorithm is proved under the same conditions of usual trust region method.
文摘Trust region methods are powerful and effective optimization methods. The conic model method is a new type of method with more information available at each iteration than standard quadratic-based methods. The advantages of the above two methods can be combined to form a more powerful method for constrained optimization. The trust region subproblem of our method is to minimize a conic function subject to the linearized constraints and trust region bound. At the same time, the new algorithm still possesses robust global properties. The global convergence of the new algorithm under standard conditions is established.
文摘In this paper, we propose a retrospective filter trust region algorithm for unconstrained optimization, which is based on the framework of the retrospective trust region method and associated with the technique of the multi-dimensional filter. The new algorithm gives a good estimation of trust region radius, relaxes the condition of accepting a trial step for the usual trust region methods. Under reasonable assumptions, we analyze the global convergence of the new method and report the preliminary results of numerical tests. We compare the results with those of the basic trust region algorithm, the filter trust region algorithm and the retrospective trust region algorithm, which shows the effectiveness of the new algorithm.
文摘In this paper, we propose and analyze a non-monotone trust region method with non-monotone line search strategy for unconstrained optimization problems. Unlike the traditional non-monotone trust region method, our algorithm utilizes non-monotone Wolfe line search to get the next point if a trial step is not adopted. Thus, it can reduce the number of solving sub-problems. Theoretical analysis shows that the new proposed method has a global convergence under some mild conditions.
文摘This paper presents a new trust region algorithm for solving a class of composite nonsmooth optimizations. It is distinguished by the fact that this method does not enforce strict monotonicity of the objective function values at successive iterates and that this method extends the existing results for this type of nonlinear optimization with smooth, or piecewise smooth, or convex objective functions or their composition. It is proved that this algorithm is globally convergent under certain conditions. Finally, some numerical results for several optimization problems are reported which show that the nonmonotonic trust region method is competitive with the usual trust region method.
文摘This paper presents a trust region two phase model algorithm for solving the equality and bound constrained nonlinear optimization problem. A concept of substationary point is given. Under suitable assumptions,the global convergence of this algorithm is proved without assuming the linear independence of the gradient of active constraints. A numerical example is also presented.
基金Supported by the National High Technology Research and Development Programme of China（ No. 2006AA04Z245 ） and China Postdoctoral Science Foundation （ No. 200904500988 ）.
文摘To overcome the shortcomings of the traditional artificial potential field method in mobile robot path planning, an improved artificial potential field model （IAPFM） was established, then a new path planning method combining the IAPFM with optimization algorithm （trust region algorithm） is proposed. Attractive force between the robot and the target location, and repulsive force between the robot and the obstacles are both converted to the potential field intensity; and filled potential field is used to guide the robot to go out of the local minimum points ; on this basis, the effect of dynamic obstacles velocity and the robot＇s velocity is consid thers and the IAPFM is established, then both the expressions of the attractive potential field and the repulsive potential field are obtained. The trust region algorithm is used to search the minimum value of the sum of all the potential field inten- sities within the movement scope which the robot can arrive in a sampling period. Connecting of all the points which hare the minimum intensity in every sampling period constitutes the global optimization path. Experiment result shows that the method can meet the real-time requirement, and is able to execute the mobile robot path planning task effectively in the dynamic environment.
基金This work was supported by the National Natural Science Foundation of China(10071037)
文摘In this paper, a new derivative free trust region method is developed based on the conic interpolation model for the unconstrained optimization. The conic interpolation model is built by means of the quadratic model function, the collinear scaling formula, quadratic approximation and interpolation. All the parameters in this model are determined by objective function interpolation condition. A new derivative free method is developed based upon this model and the global convergence of this new method is proved without any information on gradient.
文摘In this paper, we present a new line search and trust region algorithm for unconstrained optimization problems. The trust region center locates at somewhere in the negative gradient direction with the current best iterative point being on the boundary. By doing these, the trust region subproblems are constructed at a new way different with the traditional ones. Then, we test the efficiency of the new line search and trust region algorithm on some standard benchmarking. The computational results reveal that, for most test problems, the number of function and gradient calculations are reduced significantly.
文摘The trust region method plays an important role in solving optimization problems. In this paper, we propose a new nonmonotone adaptive trust region method for solving unconstrained optimization problems. Actually, we combine a popular nonmonotone technique with an adaptive trust region algorithm. The new ratio to adjusting the next trust region radius is different from the ratio in the traditional trust region methods. Under some appropriate conditions, we show that the new algorithm has good global convergence and superlinear convergence.
基金Supported by Science and Technology Foundation of Shanghai Higher Education
文摘The secant methods discussed by Fontecilla (in 1988) are considerably revised through employing a trust region multiplier strategy and introducing a nondifferentiable merit function. In this paper the secant methods are also improved by adding a dogleg typed movement which allows to overcome a phenomena similar to the Maratos effect. Furthermore, these algorithms are analyzed and global convergence theorems as well as local superlinear convergence rate are proved.
文摘In this paper, we present a regularized Newton method (M-RNM) with correction for minimizing a convex function whose Hessian matrices may be singular. At every iteration, not only a RNM step is computed but also two correction steps are computed. We show that if the objective function is LC<sup>2</sup>, then the method posses globally convergent. Numerical results show that the new algorithm performs very well.
基金supported by the Key Research Projects of China(Grant No.2022YFD2001800)the National Natural Science Foundation of China(Grant No.32071909)Zhejiang Provincial Natural Science Foundation(Grant No.LD24E05007).
文摘The film-covered sweet potato transplanting method requires ensuring the transplantation conditions of small planting holes and large lateral displacement.In the soil insertion phase,the transplantation machine requires a mechanism design with multiple timed poses,and the existing design methods are still imperfect.For this reason,this article proposes a multi-target trust region parameter-guided optimization algorithm.This algorithm aims to achieve multi-objective optimization design with more timed pose conditions starting from individual timed pose conditions.First,multi-target problems are decomposed into multiple subproblems,and the parameter arrays are kept with the minimum polymerization value of each subproblem.Then,the approximate function value reduction for each target is calculated using this parameter set,and the step size for the next iteration of each subproblem is determined by comparing this approximate reduction with the actual reduction.After many iteration calculations,the parameter arrays end the calculation when the parameter group is no longer updated.This paper uses the design of a film-covered sweet potato transplanting mechanism as a complex optimized application example.The algorithm is used to obtain the optimization results of the target values of eight groups of institutions.The smallest hole is 2.99 mm,and the horizontal transplanting distance is 108.40 mm.The maximum hole is 17.64 mm,and the horizontal transplanting distance is 124.97 mm.Considering the size of the hole and the horizontal transplanting distance of sweet potato transplanting,the mechanism’s target value of the horizontal transplanting distance at 119.92 mm and the hole size at 0.31 mm were selected to design the sweet potato transplanting machine.The correctness of the results is verified,which reflects the practicability of the algorithm.
