In this paper,we consider nonlinear infinity-norm minimization problems.We device a reliable Lagrangian dual approach for solving this kind of problems and based on this method we propose an algorithm for the mixed li...In this paper,we consider nonlinear infinity-norm minimization problems.We device a reliable Lagrangian dual approach for solving this kind of problems and based on this method we propose an algorithm for the mixed linear and nonlinear infinity- norm minimization problems.Numerical results are presented.展开更多
A class of discontinuous penalty functions was proposed to solve constrained minimization problems with the integral approach to global optimization, m-mean value and v-variance optimality conditions of a constrained ...A class of discontinuous penalty functions was proposed to solve constrained minimization problems with the integral approach to global optimization, m-mean value and v-variance optimality conditions of a constrained and penalized minimization problem were investigated. A nonsequential algorithm was proposed. Numerical examples were given to illustrate the effectiveness of the algorithm.展开更多
In reference [1], for large scale nonlinear equations , a new ODE solving method was given. This paper is a continuous work. Here has gradient structure i.e. , is a scalar function. The eigenvalues of the Jacobian of;...In reference [1], for large scale nonlinear equations , a new ODE solving method was given. This paper is a continuous work. Here has gradient structure i.e. , is a scalar function. The eigenvalues of the Jacobian of;or the Hessian of , are all real number. So the new method is very suitable for this structure. For quadratic function the convergence was proved and the spectral radius of iteration matrix was given and compared with traditional method. Examples show for large scale problems (dimension ) the new method is very efficient.展开更多
A class of variational problems with small parameters is studied. Their zeroth-order asymptotic solutions are constructed. It is shown that the zeroth-order asymptotic solution is just the minimizing sequence of varia...A class of variational problems with small parameters is studied. Their zeroth-order asymptotic solutions are constructed. It is shown that the zeroth-order asymptotic solution is just the minimizing sequence of variational problems as the small parameter approaches to zero.展开更多
This paper proposes a nonmonotonic backtracking trust region algorithm via bilevel linear programming for solving the general multicommodity minimal cost flow problems.Using the duality theory of the linear programmin...This paper proposes a nonmonotonic backtracking trust region algorithm via bilevel linear programming for solving the general multicommodity minimal cost flow problems.Using the duality theory of the linear programming and convex theory,the generalized directional derivative of the general multicommodity minimal cost flow problems is derived.The global convergence and superlinear convergence rate of the proposed algorithm are established under some mild conditions.展开更多
Minimization of transportation time is a great concern of the transportation problems like the cost minimizing transportation problems. In this writing, a transportation algorithm is developed and applied to obtain an...Minimization of transportation time is a great concern of the transportation problems like the cost minimizing transportation problems. In this writing, a transportation algorithm is developed and applied to obtain an Initial Basic Feasible Solution (IBFS) of transportation problems in minimizing transportation time. The developed method has also been illustrated numerically to test the efficiency of the method where it is observed that the proposed method yields a better result.展开更多
We study the following minimization problem d_(p)(M_(p)=∫_(R^(n))|▽u|^(2)-c|u|^(2)/|x|^(2)+V(x)|u|^(2)dx-2/p+2∫_(R^(N))|u|^p+2dx.when=p=p^(*):=4/N,,the precise concentration behavior of minimizers is analyzed as M_...We study the following minimization problem d_(p)(M_(p)=∫_(R^(n))|▽u|^(2)-c|u|^(2)/|x|^(2)+V(x)|u|^(2)dx-2/p+2∫_(R^(N))|u|^p+2dx.when=p=p^(*):=4/N,,the precise concentration behavior of minimizers is analyzed as M_(p^(*))↗‖Q_(p^(*))‖_(L^(2)),where Q_(p^(*))is the unique radially positive solution of-Δφ-cφ/|x|^(2-|φ|^(p^(*)+1)φ=0.When 0<p<p^(*)we prove that all minimizers must blow up if lim p→p^(*)M_(p)≥‖Q_(p^(*))‖L^(2).On his argument,the detailed concentration behavior of minimizers is established as p↗p^(*).展开更多
By establishing a comparison result and using monotone iterative methods, the theorem of existence for minimal and maximal solutions of periodic boundary value problems for second-order nonlinear integro-differential ...By establishing a comparison result and using monotone iterative methods, the theorem of existence for minimal and maximal solutions of periodic boundary value problems for second-order nonlinear integro-differential equations in Banach spaces is proved.展开更多
In this paper,we study the extremal problem on Cartan-egg domain of the first type by using some inequalities.The extremal mapping and extremal value between the first type of Cartan-egg domain and the unit ball when ...In this paper,we study the extremal problem on Cartan-egg domain of the first type by using some inequalities.The extremal mapping and extremal value between the first type of Cartan-egg domain and the unit ball when k≤1 and k=2,m=2 are constructed.展开更多
In this paper, we consider an extragradient thresholding algorithm for finding the sparse solution of mixed complementarity problems (MCPs). We establish a relaxation l1 regularized projection minimization model for t...In this paper, we consider an extragradient thresholding algorithm for finding the sparse solution of mixed complementarity problems (MCPs). We establish a relaxation l1 regularized projection minimization model for the original problem and design an extragradient thresholding algorithm (ETA) to solve the regularized model. Furthermore, we prove that any cluster point of the sequence generated by ETA is a solution of MCP. Finally, numerical experiments show that the ETA algorithm can effectively solve the l1 regularized projection minimization model and obtain the sparse solution of the mixed complementarity problem.展开更多
This paper proposes a modified iterative algorithm using a viscosity approximation method with a weak contraction.The purpose is to find a common element of the set of common fixed points of an infinite family of none...This paper proposes a modified iterative algorithm using a viscosity approximation method with a weak contraction.The purpose is to find a common element of the set of common fixed points of an infinite family of nonexpansive mappings and the set of a finite family of equilibrium problems that is also a solution to a variational inequality.Under suitable conditions,some strong convergence theorems are established in the framework of Hilbert spaces.The results presented in the paper improve and extend the corresponding results of Colao et al.（Colao,V.,Acedo,G.L.,and Marino,G.An implicit method for finding common solutions of variational inequalities and systems of equilibrium problems and fixed points of infinite family of nonexpansive mappings.Nonlinear Anal.71,2708–2715（2009））,Plubtieng and Punpaeng（Plubtieng,S.and Punpaeng,R.A general iterative method for equilibrium problems and fixed point problems in Hilbert spaces.J.Math.Anal.Appl.336,455–469（2007））,Colao et al.（Colao,V.,Marino,G.,and Xu,H.K.An iterative method for finding common solutions of equilibrium problem and fixed point problems.J.Math.Anal.Appl.344,340–352（2008））,Yao et al.（Yao,Y.,Liou,Y.C.,and Yao,J.C.Convergence theorem for equilibrium problems and fixed point problems of infinite family of nonexpansive mappings.Fixed Point Theory Application 2007,Article ID 64363（2007）DOI 10.1155/2007/64363）,and others.展开更多
We combine the maximum principle for vector-valued mappings established by D＇Ottavio, Leonetti and Musciano [7] with regularity results from [5] and prove the Holder continuity of the first derivatives for local mini...We combine the maximum principle for vector-valued mappings established by D＇Ottavio, Leonetti and Musciano [7] with regularity results from [5] and prove the Holder continuity of the first derivatives for local minimizers u： Ω→^R^N of splitting-type variational integrals provided Ω is a domain in R^2.展开更多
In this paper,the minimal dissipation local discontinuous Galerkin method is studied to solve the elliptic interface problems in two-dimensional domains.The interface may be arbitrary smooth curves.It is shown that th...In this paper,the minimal dissipation local discontinuous Galerkin method is studied to solve the elliptic interface problems in two-dimensional domains.The interface may be arbitrary smooth curves.It is shown that the error estimates in L;-norm for the solution and the flux are O（h;|log h|）and O(h|log h|;),respectively.In numerical experiments,the successive substitution iterative methods are used to solve the LDG schemes.Numerical results verify the efficiency and accuracy of the method.展开更多
The authors deal with the singular variational problemS(α,b,λ0)as well asS= S(α,b,λ1,λ2)where Nm/N-m+m(b-a),α,β(?)1,E= D1α,m(RN). The aim of this paper is to show the existence of minimizer for 5(α, b,λ0) an...The authors deal with the singular variational problemS(α,b,λ0)as well asS= S(α,b,λ1,λ2)where Nm/N-m+m(b-a),α,β(?)1,E= D1α,m(RN). The aim of this paper is to show the existence of minimizer for 5(α, b,λ0) and S(α,b,λ1,λ2).展开更多
文摘In this paper,we consider nonlinear infinity-norm minimization problems.We device a reliable Lagrangian dual approach for solving this kind of problems and based on this method we propose an algorithm for the mixed linear and nonlinear infinity- norm minimization problems.Numerical results are presented.
文摘A class of discontinuous penalty functions was proposed to solve constrained minimization problems with the integral approach to global optimization, m-mean value and v-variance optimality conditions of a constrained and penalized minimization problem were investigated. A nonsequential algorithm was proposed. Numerical examples were given to illustrate the effectiveness of the algorithm.
文摘In reference [1], for large scale nonlinear equations , a new ODE solving method was given. This paper is a continuous work. Here has gradient structure i.e. , is a scalar function. The eigenvalues of the Jacobian of;or the Hessian of , are all real number. So the new method is very suitable for this structure. For quadratic function the convergence was proved and the spectral radius of iteration matrix was given and compared with traditional method. Examples show for large scale problems (dimension ) the new method is very efficient.
基金supported by the National Natural Science Foundation of China (No. 10671070)the Fund for E-Institute of Shanghai Universities (No. E03004)the Open Research Fund Program of LGISEM(No. 05PJ14040)
文摘A class of variational problems with small parameters is studied. Their zeroth-order asymptotic solutions are constructed. It is shown that the zeroth-order asymptotic solution is just the minimizing sequence of variational problems as the small parameter approaches to zero.
基金the National Natural Science Foundation of China ( 1 0 4 71 0 94) ,the ScienceFoundation of Shanghai Technical Sciences Committee ( 0 2 ZA1 40 70 ) and the Science Foundation ofShanghai Education Committee( 0 2 DK0 6)
文摘This paper proposes a nonmonotonic backtracking trust region algorithm via bilevel linear programming for solving the general multicommodity minimal cost flow problems.Using the duality theory of the linear programming and convex theory,the generalized directional derivative of the general multicommodity minimal cost flow problems is derived.The global convergence and superlinear convergence rate of the proposed algorithm are established under some mild conditions.
文摘Minimization of transportation time is a great concern of the transportation problems like the cost minimizing transportation problems. In this writing, a transportation algorithm is developed and applied to obtain an Initial Basic Feasible Solution (IBFS) of transportation problems in minimizing transportation time. The developed method has also been illustrated numerically to test the efficiency of the method where it is observed that the proposed method yields a better result.
基金supported by the National Natural Science Foundation of China(11771314,12071323).
文摘We study the following minimization problem d_(p)(M_(p)=∫_(R^(n))|▽u|^(2)-c|u|^(2)/|x|^(2)+V(x)|u|^(2)dx-2/p+2∫_(R^(N))|u|^p+2dx.when=p=p^(*):=4/N,,the precise concentration behavior of minimizers is analyzed as M_(p^(*))↗‖Q_(p^(*))‖_(L^(2)),where Q_(p^(*))is the unique radially positive solution of-Δφ-cφ/|x|^(2-|φ|^(p^(*)+1)φ=0.When 0<p<p^(*)we prove that all minimizers must blow up if lim p→p^(*)M_(p)≥‖Q_(p^(*))‖L^(2).On his argument,the detailed concentration behavior of minimizers is established as p↗p^(*).
基金theNaturalScienceFoundationofEducationalCommitteeofHainanProvince China
文摘By establishing a comparison result and using monotone iterative methods, the theorem of existence for minimal and maximal solutions of periodic boundary value problems for second-order nonlinear integro-differential equations in Banach spaces is proved.
基金Supported by the SF of Jiangsu Province Education(07KJB110115)
文摘In this paper,we study the extremal problem on Cartan-egg domain of the first type by using some inequalities.The extremal mapping and extremal value between the first type of Cartan-egg domain and the unit ball when k≤1 and k=2,m=2 are constructed.
文摘In this paper, we consider an extragradient thresholding algorithm for finding the sparse solution of mixed complementarity problems (MCPs). We establish a relaxation l1 regularized projection minimization model for the original problem and design an extragradient thresholding algorithm (ETA) to solve the regularized model. Furthermore, we prove that any cluster point of the sequence generated by ETA is a solution of MCP. Finally, numerical experiments show that the ETA algorithm can effectively solve the l1 regularized projection minimization model and obtain the sparse solution of the mixed complementarity problem.
基金supported by the Natural Science Foundation of Yibin University(No.2009Z3)
文摘This paper proposes a modified iterative algorithm using a viscosity approximation method with a weak contraction.The purpose is to find a common element of the set of common fixed points of an infinite family of nonexpansive mappings and the set of a finite family of equilibrium problems that is also a solution to a variational inequality.Under suitable conditions,some strong convergence theorems are established in the framework of Hilbert spaces.The results presented in the paper improve and extend the corresponding results of Colao et al.（Colao,V.,Acedo,G.L.,and Marino,G.An implicit method for finding common solutions of variational inequalities and systems of equilibrium problems and fixed points of infinite family of nonexpansive mappings.Nonlinear Anal.71,2708–2715（2009））,Plubtieng and Punpaeng（Plubtieng,S.and Punpaeng,R.A general iterative method for equilibrium problems and fixed point problems in Hilbert spaces.J.Math.Anal.Appl.336,455–469（2007））,Colao et al.（Colao,V.,Marino,G.,and Xu,H.K.An iterative method for finding common solutions of equilibrium problem and fixed point problems.J.Math.Anal.Appl.344,340–352（2008））,Yao et al.（Yao,Y.,Liou,Y.C.,and Yao,J.C.Convergence theorem for equilibrium problems and fixed point problems of infinite family of nonexpansive mappings.Fixed Point Theory Application 2007,Article ID 64363（2007）DOI 10.1155/2007/64363）,and others.
文摘We combine the maximum principle for vector-valued mappings established by D＇Ottavio, Leonetti and Musciano [7] with regularity results from [5] and prove the Holder continuity of the first derivatives for local minimizers u： Ω→^R^N of splitting-type variational integrals provided Ω is a domain in R^2.
基金Supported by National Natural Science Foundation of China(11571002,11461046)Natural Science Foundation of Jiangxi Province,China(20151BAB211013,20161ACB21005)+2 种基金Science and Technology Project of Jiangxi Provincial Department of Education,China(150172)Science Foundation of China Academy of Engineering Physics(2015B0101021)Defense Industrial Technology Development Program(B1520133015)
文摘In this paper,the minimal dissipation local discontinuous Galerkin method is studied to solve the elliptic interface problems in two-dimensional domains.The interface may be arbitrary smooth curves.It is shown that the error estimates in L;-norm for the solution and the flux are O（h;|log h|）and O(h|log h|;),respectively.In numerical experiments,the successive substitution iterative methods are used to solve the LDG schemes.Numerical results verify the efficiency and accuracy of the method.
基金Supported by NSFC (10271118) and National Key Program for Basic Research of China(2002CCA03700)
文摘The authors deal with the singular variational problemS(α,b,λ0)as well asS= S(α,b,λ1,λ2)where Nm/N-m+m(b-a),α,β(?)1,E= D1α,m(RN). The aim of this paper is to show the existence of minimizer for 5(α, b,λ0) and S(α,b,λ1,λ2).
