As a generalization of the two-term conjugate gradient method(CGM),the spectral CGM is one of the effective methods for solving unconstrained optimization.In this paper,we enhance the JJSL conjugate parameter,initiall...As a generalization of the two-term conjugate gradient method(CGM),the spectral CGM is one of the effective methods for solving unconstrained optimization.In this paper,we enhance the JJSL conjugate parameter,initially proposed by Jiang et al.(Computational and Applied Mathematics,2021,40:174),through the utilization of a convex combination technique.And this improvement allows for an adaptive search direction by integrating a newly constructed spectral gradient-type restart strategy.Then,we develop a new spectral CGM by employing an inexact line search to determine the step size.With the application of the weak Wolfe line search,we establish the sufficient descent property of the proposed search direction.Moreover,under general assumptions,including the employment of the strong Wolfe line search for step size calculation,we demonstrate the global convergence of our new algorithm.Finally,the given unconstrained optimization test results show that the new algorithm is effective.展开更多
Spectral conjugate gradient method is an algorithm obtained by combination of spectral gradient method and conjugate gradient method,which is characterized with global convergence and simplicity of spectral gradient m...Spectral conjugate gradient method is an algorithm obtained by combination of spectral gradient method and conjugate gradient method,which is characterized with global convergence and simplicity of spectral gradient method,and small storage of conjugate gradient method.Besides,the spectral conjugate gradient method was proved that the search direction at each iteration is a descent direction of objective function even without relying on any line search method.Spectral conjugate gradient method is applied to full waveform inversion for numerical tests on Marmousi model.The authors give a comparison on numerical results obtained by steepest descent method,conjugate gradient method and spectral conjugate gradient method,which shows that the spectral conjugate gradient method is superior to the other two methods.展开更多
In this paper,a multi-product newsvendor problem is formulated as a random nonlinear integrated optimization model by taking into consideration the selling price,the producing and outsourcing quantities,and the nonlin...In this paper,a multi-product newsvendor problem is formulated as a random nonlinear integrated optimization model by taking into consideration the selling price,the producing and outsourcing quantities,and the nonlinear budget constraint.Different from the existing models,the demands of products depend on the prices,as well as being timevarying due to random market fluctuation.In addition,outsourcing strategy is adopted to deal with possible shortage caused by the limited capacity.Consequently,the constructed model is involved with joint optimization of the producing and outsourcing quantities,and the selling prices of all the products.For this model with continuous random demands,we first transform it into a nonlinear programming problem by expectation method.Then,an efficient algorithm,called the feasible-direction-based spectral conjugate gradient algorithm,is developed to find a robust solution of the model.By case study and sensitivity analysis,some interesting conclusions are drawn as follows:(a)Budget is a critical constraint for optimizing the decision-making of the retailer,and there exist different threshold values of the budget for the substitute and complementarity scenarios.(b)The price sensitivity matrix seriously affects the maximal expected profit mainly through affecting the optimal outsourcing quantity.展开更多
基金supported by the National Natural Science Foundation of China(No.72071202)the Key Laboratory of Mathematics and Engineering Applications,Ministry of Education。
文摘As a generalization of the two-term conjugate gradient method(CGM),the spectral CGM is one of the effective methods for solving unconstrained optimization.In this paper,we enhance the JJSL conjugate parameter,initially proposed by Jiang et al.(Computational and Applied Mathematics,2021,40:174),through the utilization of a convex combination technique.And this improvement allows for an adaptive search direction by integrating a newly constructed spectral gradient-type restart strategy.Then,we develop a new spectral CGM by employing an inexact line search to determine the step size.With the application of the weak Wolfe line search,we establish the sufficient descent property of the proposed search direction.Moreover,under general assumptions,including the employment of the strong Wolfe line search for step size calculation,we demonstrate the global convergence of our new algorithm.Finally,the given unconstrained optimization test results show that the new algorithm is effective.
文摘Spectral conjugate gradient method is an algorithm obtained by combination of spectral gradient method and conjugate gradient method,which is characterized with global convergence and simplicity of spectral gradient method,and small storage of conjugate gradient method.Besides,the spectral conjugate gradient method was proved that the search direction at each iteration is a descent direction of objective function even without relying on any line search method.Spectral conjugate gradient method is applied to full waveform inversion for numerical tests on Marmousi model.The authors give a comparison on numerical results obtained by steepest descent method,conjugate gradient method and spectral conjugate gradient method,which shows that the spectral conjugate gradient method is superior to the other two methods.
基金supported by National Natural Science Foundation of China(Grant No.71671190)。
文摘In this paper,a multi-product newsvendor problem is formulated as a random nonlinear integrated optimization model by taking into consideration the selling price,the producing and outsourcing quantities,and the nonlinear budget constraint.Different from the existing models,the demands of products depend on the prices,as well as being timevarying due to random market fluctuation.In addition,outsourcing strategy is adopted to deal with possible shortage caused by the limited capacity.Consequently,the constructed model is involved with joint optimization of the producing and outsourcing quantities,and the selling prices of all the products.For this model with continuous random demands,we first transform it into a nonlinear programming problem by expectation method.Then,an efficient algorithm,called the feasible-direction-based spectral conjugate gradient algorithm,is developed to find a robust solution of the model.By case study and sensitivity analysis,some interesting conclusions are drawn as follows:(a)Budget is a critical constraint for optimizing the decision-making of the retailer,and there exist different threshold values of the budget for the substitute and complementarity scenarios.(b)The price sensitivity matrix seriously affects the maximal expected profit mainly through affecting the optimal outsourcing quantity.
