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A NEWε-GENERALIZED PROJECTION METHOD OF STRONGLY SUB-FEASIBLE DIRECTIONS FOR INEQUALITY CONSTRAINED OPTIMIZATION

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Journal of Systems science & Complexity 2011年第3期24卷 604-618页

作者： Jinbao JIAN Guodong MA Chuanhao GUO college of mathematics and information science Guangxi University Nanning 530004 China Department of mathematics and Computer science Yulin Normal University Yulin 537000 China college of science Shanghai University Shanghai 200444 China.

In this paper, the nonlinear optimization problems with inequality constraints are discussed. Combining the ideas of the strongly sub-feasible directions method and the s-generalized projection technique, a new algorithm starting with an arbitrary initial iteration point for the discussed problems is presented. At each iteration, the search direction is generated by a new s-generalized projection explicit formula, and the step length is yielded by a new Armijo line search. Under some necessary assumptions, not only the algorithm possesses global and strong convergence, but also the iterative points always get into the feasible set after finite iterations. Finally, some preliminary numerical results are reported.

关键词： E-generalized projection global and strong convergence inequality constraints method of strongly sub-feasible directions optimization.

THE LIMITING CASE OF THIELE'S INTERPOLATING CONTINUED FRACTION EXPANSION

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Journal of Computational mathematics 2001年第4期19卷 433-444页

作者： Jie-qing Tan (Institute of Applied mathematics, college of science and CAD/CG Division college of Computer & information Hefei, university of Technology, Hefei 230009, china) 中国科学技术大学安徽合肥 230009

By means of the determinantal formulae for inverse and reciprocal differences with coincident data points, the limiting case of Thiele's interpolating continued fraction expansion is studied in this paper and given numerical example shows that the limiting Thiele's continued fraction expansion can be determined once for all instead of carrying out computations for each step to obtain each convergent as done in [3].

关键词： Continued fraction Inverse difference Reciprocal difference Expansion.

A characterization for a graphic sequence to be potentially C_r-graphic

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science china mathematics 2010年第11期53卷 2893-2905页

作者： YIN JianHua Department of mathematics, college of information science and Technology, Hainan university, Haikou 570228, china Department of mathematics College of Information Science and Technology Hainan University Haikou China

Let r 3, n r and π = (d1, d2, . . . , dn) be a graphic sequence. If there exists a simple graph G on n vertices having degree sequence π such that G contains Cr (a cycle of length r) as a subgraph, then π is said to be potentially Cr-graphic. Li and Yin (2004) posed the following problem: characterize π = (d1, d2, . . . , dn) such that π is potentially Cr-graphic for r 3 and n r. Rao and Rao (1972) and Kundu (1973) answered this problem for the case of n = r. In this paper, this problem is solved completely.

关键词： graph cycle degree sequence

The ε-Complexity of the Approximate Solution of Integral Equations with Isotropic Kernels

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Acta Mathematica Sinica,English Series 2002年第4期18卷 679-686页

作者： Wan MA Gen Sun FANG college of mathematics & information science of Wenzhou university, Wenzhou 325027, P. R. china Department of mathematics, Beijing normal university, Beijing 100875, P. R. china college of mathematics & information science of Wenzhou university Wenzhou P. R. China Department of mathematics Beijing Normal University Beijing P. R. China

The exact order of s-complexity is determined in L_p (2≤p≤∞) spaces for the second kind of Fredholm integral equations with kernels belonging to an isotropic Sobolev class.

关键词： Fredholm equation ε-complexity Sobolev classes

Determination of jumps for functions via derivative Gabor series

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Applied mathematics(A Journal of Chinese Universities) 2009年第2期24卷 191-199页

作者： ZHOU Ying-ying SHI Xian-liang college of mathematics and Computer science, Hunan normal university,Changsha 410081,china college of mathematics and Computer science Hunan Normal University Changsha China

Recently, Shi Xianliang and Hu Lan published the method of concentration factors for determination of jumps of functions via MCM conjugate wavelets. Usually, it is difficult to calculate the Hilbert transform of general window functions. The aim of this paper is to discuss determination of jumps for functions based on derivative Gabor series. The results will simplify the calculation of jump values.

关键词： jumps Gabor series derivative

Lp-dual Quermassintegral sums

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science china mathematics 2007年第9期50卷 1347-1360页

作者： Chang-jian ZHAO Department of information and mathematics sciences,college of science,china Jiliang university,Hangzhou 310018,china Department of information and mathematics sciences College of Science China Jiliang University Hangzhou China

In this paper,we first introduce a concept of L_p-dual Quermassintegral sum function of convex bodies and establish the polar projection Minkowski inequality and the polar projection Aleksandrov-Fenchel inequality for L_p-dual Quermassintegral ***,by using Lutwak’s width-integral of index i,we establish the L_p-Brunn-Minkowski inequality for the polar mixed projec- tion *** applications,we prove some interrelated results.

关键词： mixed volumes mixed projection bodies dual Quermassintegral sum polar of mixed projection bodies 52A40 53A15

SYSTEM OF GENERALIZED VECTOR QUASI-EQUILIBRIUM PROBLEMS ON PRODUCT FC-SPACES

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Acta Mathematica Scientia 2007年第3期27卷 522-534页

作者：丁协平 college of mathematics and Software science Sichuan Normal University

By applying a maximal element theorem on product FC-space due to author, some new equilibrium existence theorems for generalized games with fuzzy constraint correspondences are proved in FC-spaces. By using these equilibrium existence theorems, some new existence theorems of solutions for the system of generalized vector quasi-equilibrium problems are established in noncompact product FC-spaces. These results improve and generalize some recent results in literature to product FC-spaces without any convexity structure.

关键词： Maximal element generalized game equilibrium system of generalized vector quasi-equilibrium problems FC-spaces

Codimension 3 nonresonant bifurcations of homoclinic orbits with two inclination flips

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science china mathematics 2005年第2期48卷 248-260页

作者： SHUI Shuliang & ZHU Deming college of mathematics and Physics, Zhejiang normal university, Jinhua 321004, china Department of mathematics, East china normal university, Shanghai 200062, china college of mathematics and Physics Zhejiang Normal University Jinhua China Department of mathematics East China Normal University Shanghai China

Homoclinic bifurcations in four-dimensional vector fields are investigated by setting up a local coordinate near a homoclinic orbit. This homoclinic orbit is principal but its stable and unstable foliations take inclination flip. The existence, nonexistence, and uniqueness of the 1-homoclinic orbit and 1-periodic orbit are studied. The existence of the two-fold 1-periodic orbit and three-fold 1 -periodic orbit are also obtained. It is indicated that the number of periodic orbits bifurcated from this kind of homoclinic orbits depends heavily on the strength of the inclination flip.

关键词： bifurcation, homoclinic orbit, non-resonance, inclination flip, 1-periodic orbit.

MULTIPLE POSITIVE SOLUTIONS TO A SINGULAR THIRD-ORDER THREE-POINT BOUNDARY VALUE PROBLEM

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Annals of Differential Equations 2011年第3期27卷 379-383页

作者： Hongping Wu(college of Math. and information science,northwest normal university,lanzhou 730070)

In this paper,we study a singular third-order three-point boundary value problem. By a fixed point theorem of cone expansion-compression type due to Krasnosel’skii,we obtain various new results on the existence of two positive solutions to the problem,whose coefficient is allowed to have suitable singularities. Finally,we give an example to verify our results.

关键词： third-order three-point BVP positive solutions singular fixed point theorem