Due to its simplicity and efficiency,the Barzilai and Borwein(BB)gradi-ent method has received various attentions in different *** paper presents a new analysis of the BB method for two-dimensional strictly convex qua...
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Due to its simplicity and efficiency,the Barzilai and Borwein(BB)gradi-ent method has received various attentions in different *** paper presents a new analysis of the BB method for two-dimensional strictly convex quadratic *** analysis begins with the assumption that the gradient norms at the first two iterations are *** show that there is a superlinear convergence step in at most three consecutive ***,we provide a better convergence relation for the BB *** influence of the starting point and the condition number to the convergence rate is comprehensively addressed.
In this paper, we propose a new trust region affine scaling method for nonlinear programming with simple bounds. Our new method is an interior-point trust region method with a new scaling technique. The scaling matrix...
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In the field of molecular modeling and simulation, molecular surface meshes are necessary for many problems, such as molecular structure visualization and analysis, docking problem and implicit solvent modeling and si...
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In the field of molecular modeling and simulation, molecular surface meshes are necessary for many problems, such as molecular structure visualization and analysis, docking problem and implicit solvent modeling and simulation. Recently, with the developments of advanced mathematical modeling in the field of implicit solvent modeling and simulation, providing surface meshes with good qualities efficiently for large real biomolecular systems becomes an urgent issue beyond its traditional purposes for visualization and geometry analyses for molecular structure. In this review, we summarize recent works on this issue. First, various definitions of molecular surfaces and corresponding meshing methods are introduced. Second, our recent meshing tool, TMSmesh, and its performances are presented. Finally, we show the applications of the molecular surface mesh in implicit solvent modeling and simulations using boundary element method (BEM) and finite element method (FEM).
In this paper,we consider the positive semi-definite space tensor cone constrained convex program,its structure and *** study defining functions,defining sequences and polyhedral outer approximations for this positive...
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In this paper,we consider the positive semi-definite space tensor cone constrained convex program,its structure and *** study defining functions,defining sequences and polyhedral outer approximations for this positive semidefinite space tensor cone,give an error bound for the polyhedral outer approximation approach,and thus establish convergence of three polyhedral outer approximation algorithms for solving this *** then study some other approaches for solving this structured convex *** include the conic linear programming approach,the nonsmooth convex program approach and the bi-level program *** numerical examples are presented.
In this paper we propose stochastic multi-symplectic conservation law for stochastic Hamiltonian partial differential equations,and develop a stochastic multisymplectic method for numerically solving a kind of stochas...
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In this paper we propose stochastic multi-symplectic conservation law for stochastic Hamiltonian partial differential equations,and develop a stochastic multisymplectic method for numerically solving a kind of stochastic nonlinear Schrodinger *** is shown that the stochasticmulti-symplecticmethod preserves themultisymplectic structure,the discrete charge conservation law,and deduces the recurrence relation of the discrete *** experiments are performed to verify the good behaviors of the stochastic multi-symplectic method in cases of both solitary wave and collision.
The local one-dimensional multisymplectic scheme(LOD-MS)is developed for the three-dimensional(3D)Gross-Pitaevskii(GP)equation in Bose-Einstein *** idea is originated from the advantages of multisymplectic integrators...
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The local one-dimensional multisymplectic scheme(LOD-MS)is developed for the three-dimensional(3D)Gross-Pitaevskii(GP)equation in Bose-Einstein *** idea is originated from the advantages of multisymplectic integrators and from the cheap computational cost of the local one-dimensional(LOD)*** 3D GP equation is split into three linear LOD Schrodinger equations and an exactly solvable nonlinear Hamiltonian *** three linear LOD Schrodinger equations are multisymplectic which can be approximated by multisymplectic integrator(MI).The conservative properties of the proposed scheme are *** is ***,the scheme preserves the discrete local energy conservation laws and global energy conservation law if the wave function is variable *** is impossible for conventional MIs in nonlinear Hamiltonian *** numerical results show that the LOD-MS can simulate the original problems very *** are consistent with the numerical analysis.
This paper studied subspace properties of the Celis–Dennis–Tapia(CDT)subproblem that arises in some trust-region algorithms for equality constrained opti*** analysis is an extension of that presented by Wang and Yu...
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This paper studied subspace properties of the Celis–Dennis–Tapia(CDT)subproblem that arises in some trust-region algorithms for equality constrained opti*** analysis is an extension of that presented by Wang and Yuan(***.104:241–269,2006)for the standard trust-region *** suitable conditions,it is shown that the trial step obtained from the CDT subproblem is in the subspace spanned by all the gradient vectors of the objective function and of the constraints computed until the current *** on this observation,a subspace version of the Powell–Yuan trust-region algorithm is proposed for equality constrained optimization problems where the number of constraints is much lower than the number of variables. The convergence analysis is given and numerical results arealso reported.
The global boundness and existence are presented for the kind of the Rosseland equation with a general growth condition. A linearized map in a closed convex set is defined. The image set is precompact, and thus a fixe...
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The global boundness and existence are presented for the kind of the Rosseland equation with a general growth condition. A linearized map in a closed convex set is defined. The image set is precompact, and thus a fixed point exists. A multi-scale expansion method is used to obtain the homogenized equation. This equation satisfies a similar growth condition.
The linear third-order ordinary differential equation （ODE） can be transformed into a system of two second-order ODEs by introducing a variable replacement, which is different from the common order-reduced approach....
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The linear third-order ordinary differential equation （ODE） can be transformed into a system of two second-order ODEs by introducing a variable replacement, which is different from the common order-reduced approach. We choose the functions p（z） and q（x） in the variable replacement to get different cases of the special order-reduced system for the linear third-order ODE. We analyze the numerical behavior and algebraic properties of the systems of linear equations resulting from the sine diseretizations of these special second-order ODE systems. Then the block-diagonal preconditioner is used to accelerate the convergence of the Krylov subspace iteration methods for solving the discretized system of linear equation. Numerical results show that these order-reduced methods are effective for solving the linear third-order ODEs.
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