一个广义既约梯度变位算法及收敛性

对于具有非线性等式约束且变量有界的非线性规划问题，提出了一个由三阶段组成的广度既约梯度变位算法，即线性近似、既约梯度求极小和可行变位阶段．同时我们证明了该算法所具有的收敛性．     

On minimal Sturmian partial words

Partial words, which are sequences that may have some undefined positions called holes, can be viewed as sequences over an extended alphabet A_?=A∪{?}, where ? stands for a hole and matches (or is compatible with) every letter in A. The subword complexity of a partial word w, denoted by p_w(n), is the number of distinct full words (those without holes) over the alphabet that are compatible with factors of length n of w. A function f:N→N is (k,h)-feasible if for each integer N≥1, there exists a k-ary partial word w with h holes such that p_w(n)=f(n) for all n such that 1≤n≤N. We show that when dealing with feasibility in the context of finite binary partial words, the only affine functions that need investigation are f(n)=n+1 and f(n)=2n. It turns out that both are (2,h)-feasible for all non-negative integers h. We classify all minimal partial words with h holes of order N with respect to f(n)=n+1, called Sturmian, computing their lengths as well as their numbers, except when h=0 in which case we describe an algorithm that generates all minimal Sturmian full words. We show that up to reversal and complement, any minimal Sturmian partial word with one hole is of the form aⁱ?a^jba^l, where i,j,l are integers satisfying some restrictions, that all minimal Sturmian partial words with two holes are one-periodic, and that up to complement, ?(a^N−1?)^h−1 is the only minimal Sturmian partial word with h≥3 holes. Finally, we give upper bounds on the lengths of minimal partial words with respect to f(n)=2n, showing them tight for h=0,1 or 2.     

含直觉模糊弹性约束的多目标模糊线性规划求解

基于模糊结构元方法构建并讨论了一类含有直觉模糊弹性约束的多目标模糊线性规划问题.通过引入模糊数的加权特征数,定义了一种序关系并拓展了Verdegay的模糊线性规划方法,将上述多目标模糊线性规划问题转化成两个等价含参数约束条件的清晰多目标线性规划模型,并应用一种线性加权函数法给出了此类线性规划模型的对比最优可行解.最后通过一个数值实例来说明此类问题的一般求解方法.     

A FEASIBLE DIRECTION ALGORITHM WITHOUT LINE SEARCH FOR SOLVING MAX-BISECTION PROBLEMS

This paper concerns the solution of the NP-hard max-bisection problems. NCP func-tions are employed to convert max-bisection problems into continuous nonlinear program-ming problems. Solving the resulting continuous nonlinear programming problem generatesa solution that gives an upper bound on the optimal value of the max-bisection problem.From the solution, the greedy strategy is used to generate a satisfactory approximate so-lution of the max-bisection problem. A feasible direction method without line searches isproposed to solve the resulting continuous nonlinear programming, and the convergenceof the algorithm to KKT point of the resulting problem is proved. Numerical experimentsand comparisons on well-known test problems, and on randomly generated test problemsshow that the proposed method is robust, and very efficient.     

ON THE MINIMUM FEASIBLE GRAPH FOR FOUR SETS

ＯＮＴＨＥＭＩＮＩＭＵＭＦＥＡＳＩＢＬＥＧＲＡＰＨＦＯＲＦＯＵＲＳＥＴＳＸＵＹＩＮＦＥＮＧＡＮＤＦＵＸＩＡＯＢＩＮＧＡｂｓｔｒａｃｔ：ＧｉｖｅｎａｃｏｍｐｌｅｔｅｇｒａｐｈｗｉｔｈｖｅｒｔｅｘｓｅｔＸａｎｄｓｕｂｓｅｔｓＸ＿１，Ｘ＿２，．．．，Ｘ＿ｎ...     

Feasible command strategies for the control of motion of a simple mobile robot

The concept of feasible command strategies is introduced and its applicability is demonstrated by solving a guidance and control problem. This problem concerns the motion of a system which is composed of a rolling disk and a controlled slender rod that is pivoted, through its endpoint, about the disk center. The motion of the disk-rod system is subjected to state and control constraints, and it serves as a model for the motion of a simple mobile robot. In addition, the concept of path controllability is introduced and a condition is derived for the system motion path controllability. The derivation of this condition enables one to design closed-loop control laws for the system motion.     

Comment on a paper by M.C. Cheng

In a recent paper M.C. Cheng proposed new criteria for the simplex algorithm which guarantee that (i) a nonbasic variable of a basic feasible solution will remain nonbasic in an optimal basic solution, (ii) a basic variable of a basic solution will remain basic in an optimal basic solution. This comment gives (i) a slight generalization of the first result and (ii) a counterexample to the second proposition.     

Feasible Semismooth Newton Method for a Class of Stochastic Linear Complementarity Problems

We consider a class of stochastic linear complementarity problems (SLCPs) with finitely many realizations. In this paper we reformulate this class of SLCPs as a constrained minimization (CM) problem. Then, we present a feasible semismooth Newton method to solve this CM problem. Preliminary numerical results show that this CM reformulation may yield a solution with high safety for SLCPs.