An O（rL） Infeasible Interior-point Algorithm for Symmetric Cone LCP via CHKS Function

In this paper, we propose a theoretical framework of an infeasible interior-point algorithm for solving monotone linear cornplementarity problems over symmetric cones （SCLCP）. The new algorithm gets Newton-like directions from the Chen-Harker-Kanzow-Smale （CHKS） smoothing equation of the SCLCP. It possesses the following features： The starting point is easily chosen; one approximate Newton step is computed and accepted at each iteration; the iterative point with unit stepsize automatically remains in the neighborhood of central path; the iterative sequence is bounded and possesses （9（rL） polynomial-time complexity under the monotonicity and solvability of the SCLCP.     

定积分换元法的表述

就定积分换元法的表述,查阅了大量的教科书,并把它们分为六类.通过分析和举反例的方法,发现某些表述中有不必要的条件,某些表述甚至是错误的,而同济大学五版的《高等数学》中的表述更适合于工科学生.     

正弦级数L1- 收敛性确切条件的进一步研究和应用

已经对正弦级数的系数建立了一个本质上无法再推广的确切条件(对数有界变差条件) 保证其L¹- 收敛性成立. 然而, 一般来说, “全局性” 的条件在实际中是比较难以应用的. 本文进一步将条件推广到“分段性” 条件, 建立了正弦级数L¹- 收敛性的完整结果, 其重要意义在于: 第一, “全局性” 的对数有界变差条件是对单调递减条件的推广, 而本文中建立的“分段性” 的对数有界变差条件在每段中既可以推广单调递减条件, 还可以容纳单调递增条件; 第二, 可以允许所讨论的正弦级数的系数分段改变符号, 而全局性的条件要求系数不能变号; 第三, 可以允许所讨论的正弦级数的部分系数为零, 而这也是全局性的条件所无法做到的; 第四, 可用来实际构造可积的正弦级数, 这是全局性的条件比较难以做到的.     

Travelling Wave Solutions in Delayed Reaction Diffusion Systems with Partial Monotonicity

This paper deals with the existence of travelling wave fronts of delayed reaction diffusion systems with partial quasi-monotonicity. We propose a concept of ＂desirable pair of upper-lower solutions＂, through which a subset can be constructed. We then apply the Schauder＇s fixed point theorem to some appropriate operator in this subset to obtain the existence of the travelling wave fronts.     

A Constrained Optimization Approach for LCP

In this paper, LCP is converted to an equivalent nonsmooth nonlinear equation system H(x,y) = 0 by using the famous NCP function-Fischer-Burmeister function. Note that some equations in H(x, y) = 0 are nonsmooth and nonlinear hence difficult to solve while the others are linear hence easy to solve. Then we further convert the nonlinear equation system H(x, y) = 0 to an optimization problem with linear equality constraints. After that we study the conditions under which the K-T points of the optimization problem are the solutions of the original LCP and propose a method to solve the optimization problem. In this algorithm, the search direction is obtained by solving a strict convex programming at each iterative point, However, our algorithm is essentially different from traditional SQP method. The global convergence of the method is proved under mild conditions. In addition, we can prove that the algorithm is convergent superlinearly under the conditions: M is P0 matrix and the limit point is a strict complementarity solution of LCP. Preliminary numerical experiments are reported with this method.