Trust region (TR) algorithms are a class of recently developed algorithms for nonlinear optimization. A new family of TR algorithms for unconstrained optimization, which is the extension of the usual TR method, is pre...
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Trust region (TR) algorithms are a class of recently developed algorithms for nonlinear optimization. A new family of TR algorithms for unconstrained optimization, which is the extension of the usual TR method, is presented in this paper. When the objective function is bounded below and continuously, differentiable, and the norm of the Hesse approximations increases at most linearly with the iteration number, we prove the global convergence of the algorithms. Limited numerical results are reported, which indicate that our new TR algorithm is competitive.
Linear systems associated with numerical methods for constrained optimization are discussed in this paper. It is shown that the corresponding subproblems arise in most well-known methods, no matter line search methods...
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Linear systems associated with numerical methods for constrained optimization are discussed in this paper. It is shown that the corresponding subproblems arise in most well-known methods, no matter line search methods or trust region methods for constrained optimization can be expressed as similar systems of linear equations. All these linear systems can be viewed as some kinds of approximation to the linear system derived by the Lagrange-Newton method. Some properties of these linear systems are analyzed.
The Beale\|Powell restart algorithm is highly useful for large\|scale unconstrained optimization. An example is taken to show that the algorithm may fail to converge. The global convergence of a slightly modified algo...
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The Beale\|Powell restart algorithm is highly useful for large\|scale unconstrained optimization. An example is taken to show that the algorithm may fail to converge. The global convergence of a slightly modified algorithm is proved.
A multigrid solver for the steady incompressible Navier-Stokes equations on a curvilinear grid is constructed. The Cartesian velocity components are used in the discretization of the momentum equations. A staggered, g...
A multigrid solver for the steady incompressible Navier-Stokes equations on a curvilinear grid is constructed. The Cartesian velocity components are used in the discretization of the momentum equations. A staggered, geometrically symmetric distribution of velocity components is adopted which eliminates spurious pressure oscillations and facilitates the transformation between Cartesian and co-or contravariant velocity components. The SCGS (symmetrical collective Gauss-Seidel) relaxation scheme proposed by Vanka on a Cartesian grid is extended to this case to serve as the smoothing procedure of the multigrid solver, in both ''box'' and ''box-line'' versions. Due to the symmetric distribution of velocity components of this scheme, the convergence rate and numerical accuracy are not affected by grid orientation, in contrast to a scheme proposed in the literature in which difficulties arise when the grid lines turn 90-degrees from the Cartesian coordinates. Some preliminary numerical experiences with this scheme are presented. (C) 1994 Academic Press. Inc.
The DFP method is one of the most famous numerical algorithms for unconstrained optimization. For uniformly convex objective functions convergence properties of the DFP method are studied. Several conditions that can ...
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The DFP method is one of the most famous numerical algorithms for unconstrained optimization. For uniformly convex objective functions convergence properties of the DFP method are studied. Several conditions that can ensure the global convergence of the DFP method are given.
In this paper, we construct Poisson difference schemes of any order accuracy based on Pade approximation for linear Hamiltonian systems on Poisson manifolds with constant coefficients. For nonlinear Hamiltonian system...
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In this paper, we construct Poisson difference schemes of any order accuracy based on Pade approximation for linear Hamiltonian systems on Poisson manifolds with constant coefficients. For nonlinear Hamiltonian systems on Poisson manifolds, we point out that symplectic diagonal implicit Runge-Kutta methods are also Poisson schemes. The preservation of distinguished functions and quadratic first integrals of the original Hamiltonian systems of these schemes are also discussed.
The Integrated Sensing and Communications (ISAC) paradigm is anticipated to be a cornerstone of the upcoming 6G networks. In order to optimize the use of wireless resources, 6G ISAC systems need to harness the communi...
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We use formal power series to expand the method used by Yoshida in constructing explicit canonical higher order schemes for separable Hamiltonian systems and construct general higher order schemes for general dynamica...
We use formal power series to expand the method used by Yoshida in constructing explicit canonical higher order schemes for separable Hamiltonian systems and construct general higher order schemes for general dynamical systems.
We prove that the error estimates of a large class of nonconforming finite elements are dominated by their approximation errors, which means that the well-known Cea’s lemma is still valid for these nonconforming fini...
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We prove that the error estimates of a large class of nonconforming finite elements are dominated by their approximation errors, which means that the well-known Cea’s lemma is still valid for these nonconforming finite element methods. Furthermore, we derive the error estimates in both energy and L2 norms under the regularity assumption u ∈ H1+s(Ω) with any s > 0. The extensions to other related problems are possible.
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