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Equivalence of convex minimization problems over base polytopes
Springer Science and Business Media LLC - Tập 29 - Trang 519-534 - 2012
This paper considers convex optimization problems over base polytopes of polymatroids. We show that the decomposition algorithm for the separable convex function minimization problems helps us derive simple sufficient conditions for the rationality of optimal solutions, and leads us to some useful properties, including the equivalence of the lexicographically optimal base problem, introduced by Fu......
An application of Taylor models to the Nakao method on ODEs
Springer Science and Business Media LLC - Tập 26 - Trang 365-392 - 2009
The authors give short survey on validated computation of initial value problems for ODEs especially Taylor model methods. Then they propose an application of Taylor models to the Nakao method which has been developed for numerical verification methods on PDEs and apply it to initial value problems for ODEs with some numerical experiments.
A model-free shrinking-dimer saddle dynamics for finding saddle point and solution landscape
Springer Science and Business Media LLC - Tập 40 - Trang 1677-1693 - 2023
We propose a model-free shrinking-dimer saddle dynamics for finding any-index saddle points and constructing the solution landscapes, in which the force in the standard saddle dynamics is replaced by a surrogate model trained by the Gassian process learning. By this means, the exact form of the model is no longer necessary such that the saddle dynamics could be implemented based only on some obser......
Mathematical modeling analyses for obtaining an optimal railway track maintenance schedule
Springer Science and Business Media LLC - Tập 23 - Trang 207-224 - 2006
Railway track irregularities need to be kept at a satisfactory level by taking appropriate maintenance activities. This paper aims at obtaining an optimal maintenance schedule for improving the railway track irregularities using all-integer linear programming (AILP) optimization model analyses. Firstly, we try to predict a change of surface irregularities by investigating the transition process th......
PRP-like algorithm for monotone operator equations
Springer Science and Business Media LLC - Tập 38 - Trang 805-822 - 2021
Many studies have been devoted to develop and improve the iterative methods for solving convex constraint nonlinear equations problem (CCP). Based on the projection technique, we introduce a derivative-free method for approximating the solution of CCP. The proposed method is suitable for solving large-scale nonlinear equations due to its lower storage requirements. The directions generated by the ......
Message from the retiring Editor-in-Chief
Springer Science and Business Media LLC - Tập 27 - Trang 1-1 - 2010
Predator-prey dynamics with delay when prey dispersing inn-patch environment
Springer Science and Business Media LLC - Tập 20 - Trang 37-49 - 2003
A model with time delay is considered for a predator-prey system. Here, a single species disperses between n patches of a heterogeneous environment with barriers between patches while a predator does not involve a barrier between patches. It is shown that the system is permanent under some appropriate conditions, and sufficient conditions are established for the global asymptotic stability of the ......
DE-sinc method for second order singularly perturbed boundary value problems
Springer Science and Business Media LLC - Tập 26 - Trang 41-63 - 2009
In this paper the sinc-Galerkin method, as well as the sinc-collocation method, based on the double exponential transformation (DE transformation) for singularly perturbed boundary value problems of second order ordinary differential equation is considered. A large merit of the present method exists in that we can apply the standard sinc method with only a small care for perturbation parameter. Th......
Computer algebra for guaranteed accuracy. How does it help?
Springer Science and Business Media LLC - Tập 26 Số 2-3 - Trang 517-530 - 2009
Analytic continuation and Riemann surface determination of algebraic functions by computer
Springer Science and Business Media LLC - Tập 13 - Trang 107-116 - 1996
Lety=f(x) be an algebraic function which is defined as a root of bivariate polynomialP(x, y). GivenP(x, y), we present a practical computation method for analytic continuation and Riemann surface determination off(x). First, we determine the branch points off(x) by calculating the roots of a univariate polynomial numerically. Next, we expandf(x) into the Puiseux series at each branch point by the ......
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