约束优化的一个改进的强次可行SQP算法及数值试验

本文对约束优化一个强次可行SQP算法进行改进,使之产生的迭代点在有限次迭代后全落入可行域;并对算法数值效果进行了大量的比较试验.     

Chow-Witt groups and Grothendieck-Witt groups of regular schemes

Let A be a noetherian commutative Z[1/2]-algebra of Krull dimension d and let P be a projective A-module of rank d. We use derived Grothendieck-Witt groups and Euler classes to detect some obstructions for P to split off a free factor of rank one. If d?3, we show that the vanishing of its Euler class in the corresponding Grothendieck-Witt group is a necessary and sufficient condition for P to have a free factor of rank one. If d is odd, we also get some results in that direction. If A is regular, we show that the Chow-Witt groups defined by Morel and Barge appear naturally as some homology groups of a Gersten-type complex in Grothendieck-Witt theory. From this, we deduce that if d=3 then the vanishing of the Euler class of P in the corresponding Chow-Witt group is a necessary and sufficient condition for P to have a free factor of rank one.     

A hybrid descent method for solving a convex constrained optimization problem with applications

The purpose of this paper is to introduce a hybrid descent algorithm for finding a common point in fixed‐point sets of quasi‐nonexpansive mappings and solution sets of variational inequality problems. In the framework of Hilbert spaces, the strong convergence of the hybrid descent algorithm is established. Numerical experiments for the bandwidth allocation, which demonstrate the effectiveness, performance, and convergence of the proposed algorithm, are provided.     

Topological properties of strongly monotone planar vector fields

We consider strongly monotone continuous planar vector fields with a finite number of fixed points. The fixed points fall into three classes, attractors, repellers and saddles. Naturally, the relative positions of the fixed points must obey a set of restrictions imposed by monotonicity. The study of these restrictions is the main goal of the paper. With any given vector field, we associate a matrix describing the arrangement of the fixed points on the plane. We then use these matrices to formulate simple necessary and sufficient conditions which allow one to determine whether a finite set of attractors, repellers and saddles at given positions on the plane can be realized as the fixed point set of a strongly monotone vector field.     

A generalized Padé approximation method of solving homoclinic and heteroclinic orbits of strongly nonlinear autonomous oscillators

An intrinsic extension of Pad′e approximation method, called the generalized Pad′e approximation method, is proposed based on the classic Pad′e approximation theorem. According to the proposed method, the numerator and denominator of Pad′e approximant are extended from polynomial functions to a series composed of any kind of function, which means that the generalized Pad′e approximant is not limited to some forms, but can be constructed in different forms in solving different problems. Thus, many existing modifications of Pad′e approximation method can be considered to be the special cases of the proposed method. For solving homoclinic and heteroclinic orbits of strongly nonlinear autonomous oscillators, two novel kinds of generalized Pad′e approximants are constructed. Then, some examples are given to show the validity of the present method. To show the accuracy of the method, all solutions obtained in this paper are compared with those of the Runge–Kutta method.     

A high order energy preserving scheme for the strongly coupled nonlinear Schrōdinger system

A high order energy preserving scheme for a strongly coupled nonlinear Schrōdinger system is roposed by using the average vector field method. The high order energy preserving scheme is applied to simulate the soliton evolution of the strongly coupled Schrōdinger system. Numerical results show that the high order energy preserving scheme can well simulate the soliton evolution, moreover, it preserves the discrete energy of the strongly coupled nonlinear Schrōdinger system exactly.     

Toric Rigid Spaces

This paper gives a method to construct rigid spaces, which is similar to the method used to construct toric schemes.     

The core of zero-dimensional monomial ideals

The core of an ideal is the intersection of all its reductions. We describe the core of a zero-dimensional monomial ideal I as the largest monomial ideal contained in a general reduction of I. This provides a new interpretation of the core in the monomial case as well as an efficient algorithm for computing it. We relate the core to adjoints and first coefficient ideals, and in dimension two and three we give explicit formulas.     

Relative versions of some star-selection principles

We introduce some relative versions of star selection principles first considered in [5], [11]. Some of the work extends results from [4], [5] and gives some examples.