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GLOBAL CONVERGENCE AND IMPLEMENTATION OF NGTN METHOD FOR SOLVING LARGE-SCALE SMARSE NONLINEAR PROGRAMMING PROBLEMS

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Journal of Computational mathematics 2001年第4期19卷 337-346页

作者： Qin Ni (department of mathematics, Nanjing university of Aeronautics and Astronautics, Nanjing 210016, china) 南京航空航天大学江苏南京 210016

An NGTN method was proposed for solving large-scale sparse nonlinear programming (NLP) problems. This is a hybrid method of a truncated Newton direction and a modified negative gradient direction, which is suitable for handling sparse data structure and pos sesses Q-quadratic convergence rate. The global convergence of this new method is proved, the convergence rate is further analysed, and the detailed implementation is discussed in this paper. Some numerical tests for solving truss optimization and large sparse problems are reported. The theoretical and numerical results show that the new method is efficient for solving large-scale sparse NLP problems.

关键词： Nonlinear programming Large-scale problem Sparse.

A NEW PERTURBATION SIMPLEX ALGORITHM FOR LINEARPROGRAMMING

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Journal of Computational mathematics 1999年第3期17卷 233-242页

作者： Ping-qi Pan(department of Applied mathematics, Southeast university, Naming 210096, china) 东南大学应用数学系江苏南京

In this paper, we first propose a perturbation procedure for achieving dual feasibility, which starts with any basis without introducing artificial variables. This procedure and the dual simplex method are then incorporated into a general purpose algorithm; then, a modification of it using a perturbation technique is made in order to handle highly degenerate problems efficiently. Some interesting theoretical results are presented. Nmerical results obtained are reported, which are very encouraging though still preliminary.

关键词： linear programming simplex method perturbation dual feasibility

AN EXTREMAL APPROACH TO BIRKHOFF QUADRATURE FORMULAS

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Journal of Computational mathematics 2001年第5期19卷 459-466页

作者： Ying-guang Shi (department of mathematics, Hunan Normal university, Changsha 410081, china) 湖南师范大学湖南长沙 410081

Discusses an extremal problem with Birkhoff interpolation constraints. Quadrature formula derived from an extremal problem; Overview of auxiliary lemmas; Derivation of some properties of polynomials.

关键词： an extremal approach Birkhoff quadrature formulas

THE INDUCED REPRESENTATION OF C^＊-GROUPOID DYNAMIC SYSTEMS

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Chinese Annals of mathematics,Series B 1996年第1期17卷 103-114页

作者： FANG XIAOCHUN(department of mathematics, Tongji university, Shanghai 200029, china.) TONGJI UNIV DEPT MATHSHANGHAI 200029PEOPLES R CHINA

Let G be a second countable locally compact groupoid with Haar system {λu}, H be a closed subgroupoid containing Go with Haar system {λuH}. *** introduced the C*-Groupoid dynamic system (G, A, α) and its reduced crossed product Cr.d(G, A) in [2], where A is a C*-algebra, α is the homomorphism G→Aut(A). In this paper the author introduces the C*-groupoid dynamic systems (H, A, α|H) and (H\G2, A, α) induced by (G, A, α) and proves that C~*red(H, A) and C~*red(H\G2, A) are strongly Morita equivalent. Moreover the induced representation from C~*red(H, A) to C~*red(G, A) is got.

关键词： C~*-groupoid dynamic system Induced representation Haar system

(1.2)INVERSES OF OPERATORS BETWEEN BANACH SPACES AND LOCAL CONJUGACY THEOREM

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Chinese Annals of mathematics,Series B 1999年第1期20卷 57-62页

作者： MA JIPU(department of mathematics,Nanjing university,Nanjing 210093,china) Nanjing Univ Dept Math Nanjing 210093 Peoples R China

Let E and F be Banach spaces and f non-linear C1 map from E into F. The main result isTheorem 2.2, in which a connection between local conjugacy problem of f at x0E and a localfine property of f'(x) at x0(see the Definition 1.1 in this paper) are obtained. This theoremincludes as special cases the two known theorems: the finite rank theorem and Berger's Theoremfor non-linear Fredholm operators. Moreover, the thcorem gives rise the further results for somenon-linear semi-Fredholm maps and for all non-linear semi-Wedholm maps when E and F areHilbert spaces. Thus Theorem 2.2 not only just unifies the above known theorems but alsoreally generalizes them.

关键词： Nonlinear semi-Fredholm maps Conjugacy problem Banach space

TYPE X MONOTONE SYSTEMS WITH AN ORDER-INCREASING INVARIANT FUNCTION

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Chinese Annals of mathematics,Series B 1996年第3期17卷 335-342页

作者： JIANG JIFA(department of mathematics, The university of Science and Technology of china, Hefei 230036, china.) department of mathematics University of Science and Technology of China Hefei 230036 China

The author considers the asymptotic behavior of solutions of a class of ordinary dmerentialequations x = F(x) in the nonnegative orthant R7. Suppose that F(o) = o, Fi(x1,..., xn) isnondecreasing in xk for all k≠ i and that F possesses an order-increasing invarian *** it is shown that every bounded solution to such a system converges to a single equilibrium.

关键词： Type K monotone system Monotone flow Invariant function Equilibrium Convergence

ON ABELIAN AUTOMORPHISM GROUPS OF SURFACES OF GENERAL TYPE

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Chinese Annals of mathematics,Series B 1996年第1期17卷 43-52页

作者： CAI JINXING(department of mathematics, East china Normal university, Shanghai 200062, china.) E china NORMAL UNIV DEPT MATHSHANGHAI 200062PEOPLES R CHINA

It is proved that for a complex minimal smooth projective surface S of general type, its abelian automorphism group is of order≤36k2s+24, provided x(os)≥8, where Ks is the canonical divisor of S, and X(Os) the Euler... 详细信息

关键词： Projective surface Automorphism group Canonical divisor

Parabolic equation of the m-Laplacian with nonlinear boundary condition

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Chinese Science Bulletin 1998年第11期43卷 905-908页

作者： WANG Shu+ 1, 2, WANG Mingxin 3, XIE Chunhong 1 1. department of mathematics, Nanjing university, Nanjing 210093, china 2. department of mathematics, Henan university, Kaifeng 475001, china 3. department of Applied mathematics, Southeast university, department of Mathernntics Nanjing University Nanjing China department of mathematics Henan University Kaifeng China department of Applied mathematics Southeast University Nanjing China

The existence and nonexistence of global positive weak solutions of parabolic equation of the m-Laplician with nonlinear boundary condition are dealt with. The necessary and sufficient conditions on the existence of a... 详细信息

关键词： nonlinear boundary condition parabolic equation of m-Laplacian global solution blow-up.

DISSIPATIVITY AND EXPONENTIAL STABILITY OF θ-METHODS FOR SINGULARLY PERTURBED DELAY DIFFERENTIAL EQUATIONS WITH A BOUNDED LAG

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Journal of Computational mathematics 2003年第6期21卷 715-726页

作者： Hong-jiong Tian (department of mathematics, Shanghai Normal university, Shanghai 200234, china) department of mathematics Shanghai Normal University Shanghai 200234 China

This paper deals with analytic and numerical dissipativity and exponential stability of singularly perturbed delay differential equations with any bounded state-independent lag. Sufficient conditions will be presented to ensure that any solution of the singularly perturbed delay differential equations (DDEs) with a bounded lag is dissipative and exponentially stable uniformly for sufficiently small ε > 0. We will study the numerical solution defined by the linear θ-method and one-leg method and show that they are dissipative and exponentially stable uniformly for sufficiently small ε > 0 if and only if θ = 1.

关键词： Singular perturbation θ-methods Dissipativity Exponential stability.