In [3] Liu et al. investigated global convergence of conjugate gradient methods. In that paper they allowed βκ to be selected in a wider range and the global convergence of the corresponding algorithm without suffic...In [3] Liu et al. investigated global convergence of conjugate gradient methods. In that paper they allowed βκ to be selected in a wider range and the global convergence of the corresponding algorithm without sufficient decrease condition was proved. This paper investigates global convergence of nonmonotone conjugate gradient method under the same conditions.展开更多
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
A trust region method combining with nonmonotone technique is proposed tor solving symmetric nonlinear equations. The global convergence of the given method will be established under suitable conditions. Numerical res...A trust region method combining with nonmonotone technique is proposed tor solving symmetric nonlinear equations. The global convergence of the given method will be established under suitable conditions. Numerical results show that the method is interesting for the given problems.展开更多
In this paper, we propose a modified trust-region filter method algorithm for Minimax problems, which based on the framework of SQP-filter method and associated with the technique of nonmonotone method. We use the SQP...In this paper, we propose a modified trust-region filter method algorithm for Minimax problems, which based on the framework of SQP-filter method and associated with the technique of nonmonotone method. We use the SQP subproblem to acquire an attempt step, and use the filter to weigh the effect of the attempt step so as to avoid using penalty function. The algorithm uses the Lagrange function as a merit function and the nonmonotone filter to improve the effect of the algorithm. Under some mild conditions, we prove the global convergence.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
In this paper we present a nonmonotone trust region method for nonlinear least squares problems with zero-residual and prove its convergence properties. The extensive numerical results are reported which show that the...In this paper we present a nonmonotone trust region method for nonlinear least squares problems with zero-residual and prove its convergence properties. The extensive numerical results are reported which show that the nonmonotone trust region method is generally superior to the usual trust region method.展开更多
We study a new class of elliptic variational-hemivariational inequalities arising in the modelling of contact problems for elastic ideally locking materials. The contact is described by the Signorini unilateral contac...We study a new class of elliptic variational-hemivariational inequalities arising in the modelling of contact problems for elastic ideally locking materials. The contact is described by the Signorini unilateral contact condition and the friction is modelled by the nonmonotone multivalued subdifferential condition which depends on the slip. The problem is governed by a nonlinear elasticity operator, the subdifferential of the indicator function of a convex set which describes the locking constraints and a nonconvex locally Lipschitz friction potential. The result on existence and uniqueness of solution to the inequality is shown. The proof is based on a surjectivity result for maximal monotone and pseudomonotone operators combined with the application of the Banach contraction principle.展开更多
The paper presents the formulation and approximation of a static thermoelasticity problem that describes bilateral frictional contact between a deformable body and a rigid foundation. The friction is in the form of a ...The paper presents the formulation and approximation of a static thermoelasticity problem that describes bilateral frictional contact between a deformable body and a rigid foundation. The friction is in the form of a nonmonotone and multivalued law. The coupling effect of the problem is neglected. Therefore, the thermic part of the problem is considered independently on the elasticity problem. For the displacement vector, we formulate one substationary problem for a non-convex, locally Lipschitz continuous functional representing the total potential energy of the body. All problems formulated in the paper are approximated with the finite element method.展开更多
In the paper, a new mixed algorithm combined with schemes of nonmonotone line search, the systems of linear equations for higher order modification and sequential quadratic programming for constrained optimizations is...In the paper, a new mixed algorithm combined with schemes of nonmonotone line search, the systems of linear equations for higher order modification and sequential quadratic programming for constrained optimizations is presented. Under some weaker assumptions,without strict complementary condition, the algorithm is globally and superlinearly convergent.展开更多
A reaction-diffusion model for a single species with age structure and nonlocal reaction for periodic time t is derived. Some results about the model with monotone birth function are firstly introduced, and then by co...A reaction-diffusion model for a single species with age structure and nonlocal reaction for periodic time t is derived. Some results about the model with monotone birth function are firstly introduced, and then by constructing two auxiliary equations and squeezing method, the spreading speed for the system with nonmonotone birth function is obtained.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
In this paper, we propose a new method which based on the nonmonotone line search technique for solving symmetric nonlinear equations. The method can ensure that the search direction is descent for the norm function. ...In this paper, we propose a new method which based on the nonmonotone line search technique for solving symmetric nonlinear equations. The method can ensure that the search direction is descent for the norm function. Under suitable conditions, the global convergence of the method is proved. Numerical results show that the presented method is practicable for the test problems.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
The study focuses on the imputation for the longitudinal survey data which often has nonignorable nonrespondents. Local linear regression is used to impute the missing values and then the estimation of the time-depend...The study focuses on the imputation for the longitudinal survey data which often has nonignorable nonrespondents. Local linear regression is used to impute the missing values and then the estimation of the time-dependent finite populations means. The asymptotic properties (unbiasedness and consistency) of the proposed estimator are investigated. Comparisons between different parametric and nonparametric estimators are performed based on the bootstrap standard deviation, mean square error and percentage relative bias. A simulation study is carried out to determine the best performing estimator of the time-dependent finite population means. The simulation results show that local linear regression estimator yields good properties.展开更多
In this paper, an alternating direction nonmonotone approximate Newton algorithm (ADNAN) based on nonmonotone line search is developed for solving inverse problems. It is shown that ADNAN converges to a solution of th...In this paper, an alternating direction nonmonotone approximate Newton algorithm (ADNAN) based on nonmonotone line search is developed for solving inverse problems. It is shown that ADNAN converges to a solution of the inverse problems and numerical results provide the effectiveness of the proposed algorithm.展开更多
We propose two nonmonotone retraction-based proximal gradient methods for solving a class of nonconvex nonsmooth optimization problems over the Stiefel manifold.The proposed methods are equipped with the descent direc...We propose two nonmonotone retraction-based proximal gradient methods for solving a class of nonconvex nonsmooth optimization problems over the Stiefel manifold.The proposed methods are equipped with the descent direction obtained by a proximal mapping restricted in tangent space of the manifold and the BarzilaiBorwein stepsizes determined by two recent iteration points and the corresponding descent directions.By employing,respectively,the Grippo-Lampariello-Lucidi nonmonotone line search strategy and the Dai-Fletcher nonmonotone line search strategy,our proposed methods are proved to be globally convergent.Analysis on the iteration complexity for obtaining an?-stationary solution is provided.Numerical results on the sparse principle component analysis problems demonstrate the efficiency of our methods.展开更多
In this paper,a nonmonotone smoothing Newton method is proposed for solving systems of nonlinear equalities and inequalities.By constructing a new smoothing function,the problem is approximated via a family of paramet...In this paper,a nonmonotone smoothing Newton method is proposed for solving systems of nonlinear equalities and inequalities.By constructing a new smoothing function,the problem is approximated via a family of parameterized smooth equations.A smoothing Newton method is developed for solving the systems of nonlinear equalities and inequalities by adopting a modified nonmontone line search technique.And the global and local superlinear convergence of the algorithm are proved under mild assumptions.The preliminary numerical results are reported.展开更多
Nonmonotone gradient methods generally perform better than their monotone counterparts especially on unconstrained quadratic optimization.However,the known convergence rate of the monotone method is often much better ...Nonmonotone gradient methods generally perform better than their monotone counterparts especially on unconstrained quadratic optimization.However,the known convergence rate of the monotone method is often much better than its nonmonotone variant.With the aim of shrinking the gap between theory and practice of nonmonotone gradient methods,we introduce a property for convergence analysis of a large collection of gradient methods.We prove that any gradient method using stepsizes satisfying the property will converge R-linearly at a rate of 1-λ_(1)/M_(1),whereλ_(1)is the smallest eigenvalue of Hessian matrix and M_(1)is the upper bound of the inverse stepsize.Our results indicate that the existing convergence rates of many nonmonotone methods can be improved to 1-1/κwithκbeing the associated condition number.展开更多
Abstract. Conjugate gradient methods are very important methods for unconstrainedoptimization, especially for large scale problems. In this paper, we propose a new conjugategradient method, in which the technique of n...Abstract. Conjugate gradient methods are very important methods for unconstrainedoptimization, especially for large scale problems. In this paper, we propose a new conjugategradient method, in which the technique of nonmonotone line search is used. Under mildassumptions, we prove the global convergence of the method. Some numerical results arealso presented.展开更多
In this paper,an unconstrained optimization method using the nonmonotone second order Goldstein's line search is proposed.By using the negative curvature information from the Hessian,the sequence generated is show...In this paper,an unconstrained optimization method using the nonmonotone second order Goldstein's line search is proposed.By using the negative curvature information from the Hessian,the sequence generated is shown to converge to a stationary point with the second order optimality conditions.Numerical tests on a set of standard test problems confirm the efficiency of our new method.展开更多
基金Supported by the National Science Foundation of China(10171055)
文摘In [3] Liu et al. investigated global convergence of conjugate gradient methods. In that paper they allowed βκ to be selected in a wider range and the global convergence of the corresponding algorithm without sufficient decrease condition was proved. This paper investigates global convergence of nonmonotone conjugate gradient method under the same conditions.
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.
基金Supported by SF of Guangxi University(X061041)Supported by NSF of China(10761001)
文摘A trust region method combining with nonmonotone technique is proposed tor solving symmetric nonlinear equations. The global convergence of the given method will be established under suitable conditions. Numerical results show that the method is interesting for the given problems.
文摘In this paper, we propose a modified trust-region filter method algorithm for Minimax problems, which based on the framework of SQP-filter method and associated with the technique of nonmonotone method. We use the SQP subproblem to acquire an attempt step, and use the filter to weigh the effect of the attempt step so as to avoid using penalty function. The algorithm uses the Lagrange function as a merit function and the nonmonotone filter to improve the effect of the algorithm. Under some mild conditions, we prove the global convergence.
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State Major Key Project for Basic ResearchesDecision Making and Information System Laboratory+1 种基金 Academy of Science of China Natural Science Foundation of Tsinghua University.
文摘In this paper we present a nonmonotone trust region method for nonlinear least squares problems with zero-residual and prove its convergence properties. The extensive numerical results are reported which show that the nonmonotone trust region method is generally superior to the usual trust region method.
基金supported by the National Science Center of Poland under the Maestro 3 Project No.DEC-2012/06/A/ST1/00262the project Polonium“Mathematical and Numerical Analysis for Contact Problems with Friction”2014/15 between the Jagiellonian University and Universitde Perpignan Via Domitia
文摘We study a new class of elliptic variational-hemivariational inequalities arising in the modelling of contact problems for elastic ideally locking materials. The contact is described by the Signorini unilateral contact condition and the friction is modelled by the nonmonotone multivalued subdifferential condition which depends on the slip. The problem is governed by a nonlinear elasticity operator, the subdifferential of the indicator function of a convex set which describes the locking constraints and a nonconvex locally Lipschitz friction potential. The result on existence and uniqueness of solution to the inequality is shown. The proof is based on a surjectivity result for maximal monotone and pseudomonotone operators combined with the application of the Banach contraction principle.
基金supported by the Minisitry of Science of the Republic of Serbia (No. 144005)
文摘The paper presents the formulation and approximation of a static thermoelasticity problem that describes bilateral frictional contact between a deformable body and a rigid foundation. The friction is in the form of a nonmonotone and multivalued law. The coupling effect of the problem is neglected. Therefore, the thermic part of the problem is considered independently on the elasticity problem. For the displacement vector, we formulate one substationary problem for a non-convex, locally Lipschitz continuous functional representing the total potential energy of the body. All problems formulated in the paper are approximated with the finite element method.
文摘In the paper, a new mixed algorithm combined with schemes of nonmonotone line search, the systems of linear equations for higher order modification and sequential quadratic programming for constrained optimizations is presented. Under some weaker assumptions,without strict complementary condition, the algorithm is globally and superlinearly convergent.
基金Supported by the NSF of China(11171120)Supported by the Doctoral Program of Higher Education of China(20094407110001)Supported by the NSF of Guangdong Province(10151063101000003)
文摘A reaction-diffusion model for a single species with age structure and nonlocal reaction for periodic time t is derived. Some results about the model with monotone birth function are firstly introduced, and then by constructing two auxiliary equations and squeezing method, the spreading speed for the system with nonmonotone birth function is obtained.
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In this paper, we propose a new method which based on the nonmonotone line search technique for solving symmetric nonlinear equations. The method can ensure that the search direction is descent for the norm function. Under suitable conditions, the global convergence of the method is proved. Numerical results show that the presented method is practicable for the test problems.
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.
文摘The study focuses on the imputation for the longitudinal survey data which often has nonignorable nonrespondents. Local linear regression is used to impute the missing values and then the estimation of the time-dependent finite populations means. The asymptotic properties (unbiasedness and consistency) of the proposed estimator are investigated. Comparisons between different parametric and nonparametric estimators are performed based on the bootstrap standard deviation, mean square error and percentage relative bias. A simulation study is carried out to determine the best performing estimator of the time-dependent finite population means. The simulation results show that local linear regression estimator yields good properties.
文摘In this paper, an alternating direction nonmonotone approximate Newton algorithm (ADNAN) based on nonmonotone line search is developed for solving inverse problems. It is shown that ADNAN converges to a solution of the inverse problems and numerical results provide the effectiveness of the proposed algorithm.
基金supported by the National Natural Science Foundation of China(Grant Nos.11671116,12071108 and 11701137)Natural Science Foundation of Hebei Province(Grant No.A2021202010)。
文摘We propose two nonmonotone retraction-based proximal gradient methods for solving a class of nonconvex nonsmooth optimization problems over the Stiefel manifold.The proposed methods are equipped with the descent direction obtained by a proximal mapping restricted in tangent space of the manifold and the BarzilaiBorwein stepsizes determined by two recent iteration points and the corresponding descent directions.By employing,respectively,the Grippo-Lampariello-Lucidi nonmonotone line search strategy and the Dai-Fletcher nonmonotone line search strategy,our proposed methods are proved to be globally convergent.Analysis on the iteration complexity for obtaining an?-stationary solution is provided.Numerical results on the sparse principle component analysis problems demonstrate the efficiency of our methods.
基金supported by the National Natural Science Foundation of China(No.12361064,No.52275504 and No.11871383)Hubei Province Key Laboratory of Systems Science in Metallurgical Process(Wuhan University of Science and Technology)(No.Y201905 and No.z202301)。
文摘In this paper,a nonmonotone smoothing Newton method is proposed for solving systems of nonlinear equalities and inequalities.By constructing a new smoothing function,the problem is approximated via a family of parameterized smooth equations.A smoothing Newton method is developed for solving the systems of nonlinear equalities and inequalities by adopting a modified nonmontone line search technique.And the global and local superlinear convergence of the algorithm are proved under mild assumptions.The preliminary numerical results are reported.
基金supported by the National Natural Science Foundation of China(No.11701137)the Natural Science Foundation of Hebei Province(No.A2021202010).
文摘Nonmonotone gradient methods generally perform better than their monotone counterparts especially on unconstrained quadratic optimization.However,the known convergence rate of the monotone method is often much better than its nonmonotone variant.With the aim of shrinking the gap between theory and practice of nonmonotone gradient methods,we introduce a property for convergence analysis of a large collection of gradient methods.We prove that any gradient method using stepsizes satisfying the property will converge R-linearly at a rate of 1-λ_(1)/M_(1),whereλ_(1)is the smallest eigenvalue of Hessian matrix and M_(1)is the upper bound of the inverse stepsize.Our results indicate that the existing convergence rates of many nonmonotone methods can be improved to 1-1/κwithκbeing the associated condition number.
基金the National Natural Science Foundation of China(19801033,10171104).
文摘Abstract. Conjugate gradient methods are very important methods for unconstrainedoptimization, especially for large scale problems. In this paper, we propose a new conjugategradient method, in which the technique of nonmonotone line search is used. Under mildassumptions, we prove the global convergence of the method. Some numerical results arealso presented.
基金This work was supported by the National Natural Science Foundation of China(Grant No.10231060)the Specialized Research Fund of Doctoral Program of Higher Education of China(Grant No.20040319003)
文摘In this paper,an unconstrained optimization method using the nonmonotone second order Goldstein's line search is proposed.By using the negative curvature information from the Hessian,the sequence generated is shown to converge to a stationary point with the second order optimality conditions.Numerical tests on a set of standard test problems confirm the efficiency of our new method.
