In this paper, we propose several new line search rules for solving unconstrained minimization problems. These new line search rules can extend the accepted scope of step sizes to a wider extent than the corresponding...In this paper, we propose several new line search rules for solving unconstrained minimization problems. These new line search rules can extend the accepted scope of step sizes to a wider extent than the corresponding original ones and give an adequate initial step size at each iteration. It is proved that the resulting line search algorithms have global convergence under some mild conditions. It is also proved that the search direction plays an important role in line search methods and that the step size approaches mainly guarantee global convergence in general cases. The convergence rate of these methods is also investigated. Some numerical results show that these new line search algorithms are effective in practical computation.展开更多
In this paper, a new class of three term memory gradient method with non-monotone line search technique for unconstrained optimization is presented. Global convergence properties of the new methods are discussed. Comb...In this paper, a new class of three term memory gradient method with non-monotone line search technique for unconstrained optimization is presented. Global convergence properties of the new methods are discussed. Combining the quasi-Newton method with the new method, the former is modified to have global convergence property. Numerical results show that the new algorithm 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
In this paper, a new steplength formula is proposed for unconstrained optimization,which can determine the step-size only by one step and avoids the line search step. Global convergence of the five well-known conjugat...In this paper, a new steplength formula is proposed for unconstrained optimization,which can determine the step-size only by one step and avoids the line search step. Global convergence of the five well-known conjugate gradient methods with this formula is analyzed,and the corresponding results are as follows：（1） The DY method globally converges for a strongly convex LC^1 objective function;（2） The CD method, the FR method, the PRP method and the LS method globally converge for a general, not necessarily convex, LC^1 objective function.展开更多
In this paper we consider the global convergence of any conjugate gradient method of the form d1=-g1,dk+1=-gk+1+βkdk(k≥1)with any βk satisfying sume conditions,and with the strong wolfe line search conditions.Under...In this paper we consider the global convergence of any conjugate gradient method of the form d1=-g1,dk+1=-gk+1+βkdk(k≥1)with any βk satisfying sume conditions,and with the strong wolfe line search conditions.Under the convex assumption on the objective function,we preve the descenf property and the global convergence of this method.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
In this paper, we provide and analyze a new scaled conjugate gradient method and its performance, based on the modified secant equation of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method and on a new modified nonmo...In this paper, we provide and analyze a new scaled conjugate gradient method and its performance, based on the modified secant equation of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method and on a new modified nonmonotone line search technique. The method incorporates the modified BFGS secant equation in an effort to include the second order information of the objective function. The new secant equation has both gradient and function value information, and its update formula inherits the positive definiteness of Hessian approximation for general convex function. In order to improve the likelihood of finding a global optimal solution, we introduce a new modified nonmonotone line search technique. It is shown that, for nonsmooth convex problems, the proposed algorithm is globally convergent. Numerical results show that this new scaled conjugate gradient algorithm is promising and efficient for solving not only convex but also some large scale nonsmooth nonconvex problems in the sense of the Dolan-Moré performance profiles.展开更多
In this paper, we present a nonmonotone smoothing Newton algorithm for solving the circular cone programming(CCP) problem in which a linear function is minimized or maximized over the intersection of an affine space w...In this paper, we present a nonmonotone smoothing Newton algorithm for solving the circular cone programming(CCP) problem in which a linear function is minimized or maximized over the intersection of an affine space with the circular cone. Based on the relationship between the circular cone and the second-order cone(SOC), we reformulate the CCP problem as the second-order cone problem(SOCP). By extending the nonmonotone line search for unconstrained optimization to the CCP, a nonmonotone smoothing Newton method is proposed for solving the CCP. Under suitable assumptions, the proposed algorithm is shown to be globally and locally quadratically convergent. Some preliminary numerical results indicate the effectiveness of the proposed algorithm for solving the CCP.展开更多
In this paper, we extend a descent algorithm without line search for solving unconstrained optimization problems. Under mild conditions, its global convergence is established. Further, we generalize the search directi...In this paper, we extend a descent algorithm without line search for solving unconstrained optimization problems. Under mild conditions, its global convergence is established. Further, we generalize the search direction to more general form, and also obtain the global convergence of corresponding algorithm. The numerical results illustrate that the new algorithm is effective.展开更多
In this paper, the Eigenvalue Complementarity Problem (EiCP) with real symmetric matrices is addressed, which appears in the study of contact problem in mechanics. We discuss a quadratic programming formulation to the...In this paper, the Eigenvalue Complementarity Problem (EiCP) with real symmetric matrices is addressed, which appears in the study of contact problem in mechanics. We discuss a quadratic programming formulation to the problem. The resulting problems are nonlinear programs that can be solved by a line search filter-SQP algorithm.展开更多
In recent years, Japan, and especially rural areas have faced the growing problems of debt-ridden local railway lines along with the population decline and aging population. Therefore, it is best to consider the disco...In recent years, Japan, and especially rural areas have faced the growing problems of debt-ridden local railway lines along with the population decline and aging population. Therefore, it is best to consider the discontinuation of local railway lines and introduce replacement buses to secure the transportation methods of the local people especially in rural areas. Based on the above background, targeting local railway lines that may be discontinued in the near future, appropriate bus stops when provided with potential bus stops were selected, the present study proposed a method that introduces routes for railway replacement buses adopting ant colony optimization (ACO). The improved ACO was designed and developed based on the requirements set concerning the route length, number of turns, road width, accessibility of railway lines and zones without bus stops as well as the constraint conditions concerning the route length, number of turns and zones without bus stops. Original road network data were generated and processed adopting a geographic information systems (GIS), and these are used to search for the optimal route for railway replacement buses adopting the improved ACO concerning the 8 zones on the target railway line (JR Kakogawa line). By comparing the improved ACO with Dijkstra’s algorithm, its relevance was verified and areas needing further improvements were revealed.展开更多
In this paper, the non-quasi-Newton＇s family with inexact line search applied to unconstrained optimization problems is studied. A new update formula for non-quasi-Newton＇s family is proposed. It is proved that the ...In this paper, the non-quasi-Newton＇s family with inexact line search applied to unconstrained optimization problems is studied. A new update formula for non-quasi-Newton＇s family is proposed. It is proved that the constituted algorithm with either Wolfe-type or Armijotype line search converges globally and Q-superlinearly if the function to be minimized has Lipschitz continuous gradient.展开更多
Recently, Gilbert and Nocedal([3]) investigated global convergence of conjugate gradient methods related to Polak-Ribiere formular, they restricted beta(k) to non-negative value. [5] discussed the same problem as that...Recently, Gilbert and Nocedal([3]) investigated global convergence of conjugate gradient methods related to Polak-Ribiere formular, they restricted beta(k) to non-negative value. [5] discussed the same problem as that in [3] and relaxed beta(k) to be negative with the objective function being convex. This paper allows beta(k) to be selected in a wider range than [5]. Especially, the global convergence of the corresponding algorithm without sufficient decrease condition is proved.展开更多
This paper discusses the global convergence of a class of nonmonotone conjugate gra- dient methods(NM methods) for nonconvex object functions.This class of methods includes the nonmonotone counterpart of modified Po...This paper discusses the global convergence of a class of nonmonotone conjugate gra- dient methods(NM methods) for nonconvex object functions.This class of methods includes the nonmonotone counterpart of modified Polak- Ribière method and modified Hestenes- Stiefel method as special cases展开更多
A hybrid method of the Polak-Ribière-Polyak (PRP) method and the Wei-Yao-Liu (WYL) method is proposed for unconstrained optimization pro- blems, which possesses the following properties: i) This method inherits a...A hybrid method of the Polak-Ribière-Polyak (PRP) method and the Wei-Yao-Liu (WYL) method is proposed for unconstrained optimization pro- blems, which possesses the following properties: i) This method inherits an important property of the well known PRP method: the tendency to turn towards the steepest descent direction if a small step is generated away from the solution, preventing a sequence of tiny steps from happening;ii) The scalar holds automatically;iii) The global convergence with some line search rule is established for nonconvex functions. Numerical results show that the method is effective for the test problems.展开更多
By using Fukushima's differentiable merit function,Taji,Fukushima and Ibaraki have given a globally convergent modified Newton method for the strongly monotone variational inequality problem and proved their metho...By using Fukushima's differentiable merit function,Taji,Fukushima and Ibaraki have given a globally convergent modified Newton method for the strongly monotone variational inequality problem and proved their method to be quadratically convergent under certain assumptions in 1993.In this paper a hybrid method for the variational inequality problem under the assumptions that the mapping F is continuously differentiable and its Jacobian matrix Δ F(x) is positive definite for all x∈S rather than strongly monotone and that the set S is nonempty,polyhedral,closed and convex is proposed.Armijo type line search and trust region strategies as well as Fukushima's differentiable merit function are incorporated into the method.It is then shown that the method is well defined and globally convergent and that,under the same assumptions as those of Taji et al.,the method reduces to the basic Newton method and hence the rate of convergence is quadratic.Computational experiences show the efficiency of the proposed method.展开更多
In this paper, a new conjugate gradient formula and its algorithm for solving unconstrained optimization problems are proposed. The given formula satisfies with satisfying the descent condition. Under the Grippo-Lucid...In this paper, a new conjugate gradient formula and its algorithm for solving unconstrained optimization problems are proposed. The given formula satisfies with satisfying the descent condition. Under the Grippo-Lucidi line search, the global convergence property of the given method is discussed. The numerical results show that the new method is efficient for the given test problems.展开更多
文摘In this paper, we propose several new line search rules for solving unconstrained minimization problems. These new line search rules can extend the accepted scope of step sizes to a wider extent than the corresponding original ones and give an adequate initial step size at each iteration. It is proved that the resulting line search algorithms have global convergence under some mild conditions. It is also proved that the search direction plays an important role in line search methods and that the step size approaches mainly guarantee global convergence in general cases. The convergence rate of these methods is also investigated. Some numerical results show that these new line search algorithms are effective in practical computation.
文摘In this paper, a new class of three term memory gradient method with non-monotone line search technique for unconstrained optimization is presented. Global convergence properties of the new methods are discussed. Combining the quasi-Newton method with the new method, the former is modified to have global convergence property. Numerical results show that the new algorithm 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(Grant No.11761014)the Natural Science Foundation of Guangxi Zhuang Autonomous Region(Grant No.2017GXNSFAA198243)+2 种基金Guangxi Basic Ability Improvement Project for the Middle-Aged and Young Teachers of Colleges and Universities(Grant Nos.2017KY0068KY2016YB069)Guangxi Higher Education Undergraduate Course Teaching Reform Project(Grant No.2017JGB147)
文摘In this paper, a new steplength formula is proposed for unconstrained optimization,which can determine the step-size only by one step and avoids the line search step. Global convergence of the five well-known conjugate gradient methods with this formula is analyzed,and the corresponding results are as follows：（1） The DY method globally converges for a strongly convex LC^1 objective function;（2） The CD method, the FR method, the PRP method and the LS method globally converge for a general, not necessarily convex, LC^1 objective function.
基金This work is supported by the National Natural Science Foundation of China
文摘In this paper we consider the global convergence of any conjugate gradient method of the form d1=-g1,dk+1=-gk+1+βkdk(k≥1)with any βk satisfying sume conditions,and with the strong wolfe line search conditions.Under the convex assumption on the objective function,we preve the descenf property and the global convergence of this method.
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In this paper, we provide and analyze a new scaled conjugate gradient method and its performance, based on the modified secant equation of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method and on a new modified nonmonotone line search technique. The method incorporates the modified BFGS secant equation in an effort to include the second order information of the objective function. The new secant equation has both gradient and function value information, and its update formula inherits the positive definiteness of Hessian approximation for general convex function. In order to improve the likelihood of finding a global optimal solution, we introduce a new modified nonmonotone line search technique. It is shown that, for nonsmooth convex problems, the proposed algorithm is globally convergent. Numerical results show that this new scaled conjugate gradient algorithm is promising and efficient for solving not only convex but also some large scale nonsmooth nonconvex problems in the sense of the Dolan-Moré performance profiles.
基金supported by the National Natural Science Foundation of China(11401126,71471140 and 11361018)Guangxi Natural Science Foundation(2016GXNSFBA380102 and 2014GXNSFFA118001)+2 种基金Guangxi Key Laboratory of Cryptography and Information Security(GCIS201618)Guangxi Key Laboratory of Automatic Detecting Technology and Instruments(YQ15112 and YQ16112)China
文摘In this paper, we present a nonmonotone smoothing Newton algorithm for solving the circular cone programming(CCP) problem in which a linear function is minimized or maximized over the intersection of an affine space with the circular cone. Based on the relationship between the circular cone and the second-order cone(SOC), we reformulate the CCP problem as the second-order cone problem(SOCP). By extending the nonmonotone line search for unconstrained optimization to the CCP, a nonmonotone smoothing Newton method is proposed for solving the CCP. Under suitable assumptions, the proposed algorithm is shown to be globally and locally quadratically convergent. Some preliminary numerical results indicate the effectiveness of the proposed algorithm for solving the CCP.
文摘In this paper, we extend a descent algorithm without line search for solving unconstrained optimization problems. Under mild conditions, its global convergence is established. Further, we generalize the search direction to more general form, and also obtain the global convergence of corresponding algorithm. The numerical results illustrate that the new algorithm is effective.
文摘In this paper, the Eigenvalue Complementarity Problem (EiCP) with real symmetric matrices is addressed, which appears in the study of contact problem in mechanics. We discuss a quadratic programming formulation to the problem. The resulting problems are nonlinear programs that can be solved by a line search filter-SQP algorithm.
文摘In recent years, Japan, and especially rural areas have faced the growing problems of debt-ridden local railway lines along with the population decline and aging population. Therefore, it is best to consider the discontinuation of local railway lines and introduce replacement buses to secure the transportation methods of the local people especially in rural areas. Based on the above background, targeting local railway lines that may be discontinued in the near future, appropriate bus stops when provided with potential bus stops were selected, the present study proposed a method that introduces routes for railway replacement buses adopting ant colony optimization (ACO). The improved ACO was designed and developed based on the requirements set concerning the route length, number of turns, road width, accessibility of railway lines and zones without bus stops as well as the constraint conditions concerning the route length, number of turns and zones without bus stops. Original road network data were generated and processed adopting a geographic information systems (GIS), and these are used to search for the optimal route for railway replacement buses adopting the improved ACO concerning the 8 zones on the target railway line (JR Kakogawa line). By comparing the improved ACO with Dijkstra’s algorithm, its relevance was verified and areas needing further improvements were revealed.
文摘In this paper, the non-quasi-Newton＇s family with inexact line search applied to unconstrained optimization problems is studied. A new update formula for non-quasi-Newton＇s family is proposed. It is proved that the constituted algorithm with either Wolfe-type or Armijotype line search converges globally and Q-superlinearly if the function to be minimized has Lipschitz continuous gradient.
文摘Recently, Gilbert and Nocedal([3]) investigated global convergence of conjugate gradient methods related to Polak-Ribiere formular, they restricted beta(k) to non-negative value. [5] discussed the same problem as that in [3] and relaxed beta(k) to be negative with the objective function being convex. This paper allows beta(k) to be selected in a wider range than [5]. Especially, the global convergence of the corresponding algorithm without sufficient decrease condition is proved.
基金Supported by the National Natural Science Foundation of China(1 0 1 6 1 0 0 2 ) and Guangxi Natural Sci-ence Foundation (0 1 3 5 0 0 4 )
文摘This paper discusses the global convergence of a class of nonmonotone conjugate gra- dient methods(NM methods) for nonconvex object functions.This class of methods includes the nonmonotone counterpart of modified Polak- Ribière method and modified Hestenes- Stiefel method as special cases
文摘A hybrid method of the Polak-Ribière-Polyak (PRP) method and the Wei-Yao-Liu (WYL) method is proposed for unconstrained optimization pro- blems, which possesses the following properties: i) This method inherits an important property of the well known PRP method: the tendency to turn towards the steepest descent direction if a small step is generated away from the solution, preventing a sequence of tiny steps from happening;ii) The scalar holds automatically;iii) The global convergence with some line search rule is established for nonconvex functions. Numerical results show that the method is effective for the test problems.
基金Project supported by the National Natural Science Foundation of China (1 9971 0 65)
文摘By using Fukushima's differentiable merit function,Taji,Fukushima and Ibaraki have given a globally convergent modified Newton method for the strongly monotone variational inequality problem and proved their method to be quadratically convergent under certain assumptions in 1993.In this paper a hybrid method for the variational inequality problem under the assumptions that the mapping F is continuously differentiable and its Jacobian matrix Δ F(x) is positive definite for all x∈S rather than strongly monotone and that the set S is nonempty,polyhedral,closed and convex is proposed.Armijo type line search and trust region strategies as well as Fukushima's differentiable merit function are incorporated into the method.It is then shown that the method is well defined and globally convergent and that,under the same assumptions as those of Taji et al.,the method reduces to the basic Newton method and hence the rate of convergence is quadratic.Computational experiences show the efficiency of the proposed method.
文摘In this paper, a new conjugate gradient formula and its algorithm for solving unconstrained optimization problems are proposed. The given formula satisfies with satisfying the descent condition. Under the Grippo-Lucidi line search, the global convergence property of the given method is discussed. The numerical results show that the new method is efficient for the given test problems.
