Superlinearly Convergent Infeasible-Interior-Point Algorithm for Degenerate LCP

A large-step infeasible path-following method is proposed for solving general linear complementarity problems with sufficient matrices. If the problem has a solution, the algorithm is superlinearly convergent from any positive starting points, even for degenerate problems. The algorithm generates points in a large neighborhood of the central path. Each iteration requires only one matrix factorization and at most three (asymptotically only two) backsolves. It has been recently proved that any sufficient matrix is a P _*()-matrix for some 0. The computational complexity of the algorithm depends on as well as on a feasibility measure of the starting point. If the starting point is feasible or close to being feasible, then the iteration complexity is . Otherwise, for arbitrary positive and large enough starting points, the iteration complexity is O((1 + )² nL). We note that, while computational complexity depends on , the algorithm itself does not.     

Multiplicity of nodal solutions for elliptic problems involving non-odd nonlinearities

In this paper, we study the effect of domain shape on the number of 2-nodal solutions for the semilinear elliptic equation involving non-odd nonlinearities. We prove that a semilinear elliptic equation in an m$m$-bump domain (possibly unbounded) has m²$m^2$ 2-nodal solutions and we can find a least energy nodal solution in those solutions. Furthermore, we can describe the bump location of these solutions.     

光纤非线性效应对10 Gb/s波分复用色散补偿系统的限制

对信道间距为１００ＧＨｚ的８倍１０Ｇｂ／ｓ波分复用色散补偿系统进行了计算机仿真,分析了光纤的色散和自相位调制（ＳＰＭ）、互相位调制（ＸＰＭ）、四波混频（ＦＷＭ）等非线性效应在具有级联光放大器系统中的作用。四种色散补偿方案是：ＳＭＦ（常规单模光纤）＋ＤＣＦ１（色散斜率为正的色散补偿光纤）、ＳＭＦ＋ＤＣＦ２（色散斜率为负的色散补偿光纤）、ＴＷ１（色散为正的非零色散光纤）＋ＴＷ２（色散为负的非零色散光纤     

Constitutive theories for nonlocal micropolar continua with implicity and with multiple interactions

In this paper the constitutive theory for nonlocal micropolar continua which was proposed by A. C. Eringen is extended to the cases for nonlocal micropolar continua with implicity and with multiple interactions. Here nonlocal micropolar thermoelastic solids with implicity and with multiple interactions are cited as instances to illustrate the procedure for the establishment of their constitutive theories as well as two relevant theorems concerning the constitutive theories for those solids are given.     

用半光滑牛顿法求解一般的凸光顺问题

本文讨论一般的凸光顺问题minF（y）：=∫a^b（｜D^k y｜）^2dt＋∑（i=1）^N ωi｜y（ti）-zi｜^2．其中,忌芝3而且可在闭凸集凡K（∪→）L2^k[a,b]．我们把该问题转化为半光滑方程组并给出一个求解该方程组的半光滑牛顿算法．最后证明算法的超线性收敛性并给出数值算例．     

非拟牛顿非凸族的收敛性

１．引言 对于无约束最优化问题拟牛顿法是目前最成熟,应用最广泛的解法之一．近二十多年来,对拟牛顿法收敛性质的研究一直是非线性最优化算法理论研究的热点．带非精确搜索的拟牛顿算法的研究是从１９７６年 Ｐｏｗｅｌｌ［１］开始,他证明了带 Ｗｏｌｆｅ搜索 ＢＦＧＳ算法的全局收敛性和超线性收敛性． １９７８年 Ｂｙｒｄ, Ｎｏｃｅｄａｌ; Ｙａ－Ｘｉａｎｇ Ｙｕａｎ［３］成功地将 Ｐｏｗｅｌｌ的结果推广到限制的 Ｂｒｏｓｄｅｎ凸族． １９８９年, Ｎｏｃｅｄａｌ［４］在目标函数一致凸的条件下,证明了带回追搜索的ＢＦＧ…     

A hydrodynamic approach to multidimensional dissipation-based Schrödinger models from quantum Fokker-Planck dynamics

In this paper we are concerned with the modeling of quantum dissipation and diffusion effects at the level of the multidimensional Schrödinger equation. Our starting point is the quantum Fokker-Planck master equation describing dissipative interactions (of mass and energy) of the particle ensemble with a thermal bath in thermodynamic equilibrium. When considering its associated hydrodynamic system, which rules the temporal evolution of the local density and the mean fluid-flow velocity, and imposing physically admissible closure relations, these equations can be seen as describing the fluid-mechanical evolution of the macroscopic amplitude and phase of an envelope wavefunction, thus giving rise to a family of dissipative Schrödinger equations of logarithmic type whose steady state and radial dynamics are analyzed. Also, numerical comparison with the exactly solvable models for the free particle and the damped harmonic oscillator is performed.