Global optimality conditions for quadratic 0–1 programming with inequality constraints

Quadratic 0-1 problems with linear inequality constraints are briefly considered in this paper.Global optimality conditions for these problems,including a necessary condition and some sufficient conditions,are presented.The necessary condition is expressed without dual variables.The relations between the global optimal solutions of nonconvex quadratic 0-1 problems and the associated relaxed convex problems are also studied.     

贪心核加速动态规划算法精确求解适用范围

针对背包容量折扣系数在 0.8~0.9 时,贪心核加速动态规划算法（GCADP）无法求得逆向强相关折扣｛0-1｝背包问题实例（IDKP）精确解的问题,为求得 D｛0-1｝KP 实例的精确解,在对 IDKP 实例参数进行分析的基础上,给出 GCADP 算法能精确求解 D｛0-1｝KP 实例的限定条件：任意项集的价值系数满足价值最小项大于价值次大项的 0.99 倍。将该条件应用到 4 类 D｛0-1｝KP 实例的参数设置中,生成新的大规模 D｛0-1｝KP 实 例。对 4 类 D｛0-1｝KP 实例运用 GCADP 和动态规划（DP）进行计算,计算结果表明,新的 4 类 D｛0-1｝KP 实例均得到精确解,并且 GCADP 随着数据规模的变大,求解时长增长平缓。     

线性规划非单调一阶段算法

为了获取计算的高效率，有必要修正单纯形算法的原则．本提出了一个新的单纯形一阶段算法．与传统单纯形算法不同的是，新算法不仅不要求目标函数值单调变化，且在一阶段的迭代过程中也不必保持变量的可行性，而是采用纯组合的方法去达到可行．这样摆脱了迭代时的比值检验，减少了每次迭代的计算工组量．理论分析及数值计算结果表明新算法的前景令人鼓舞．     

用动态规划法和贪心法解决背包问题

0-1背包问题和背包问题是一类经典的NP困难问题。采用动态规划法和贪心法对该问题进行求解,分析和比较这两种算法在求解同一问题时的差异。     

线性规划唯一最优解的讨论

本文给出线性规划问题最优解唯一的三个充要条件和一个充分条件，从而弥补教材在这方面的不足。     

必要条件假言命题若干问题新探

就必要条件假言命题的汉语表达式及其分类、判定真假依据、负命题的等值式，以及以此类命题作前提的反三段论等问题，作出了全新的探讨。归纳出16种汉语表达式，并加以分类；认为：必要条件假言命题的真假只能依据其前、后件之间客观上是否具有必要条件关系之标准来判定；认为p←q实即→p→□→q，其否定式是“→p∧→□→q”，而不是“→p∧q”；揭示了必要条件反三段论的内涵、逻辑结构，并给出了它的有效推理式。     

非线性混合整数规划的罚函数解法

文[6]中，我们对非线性混合整数规划的解法进行了探讨，利用罚函数把有约束非线性混合整数规划问题化为等价的无约束非线性混合整数规划问题，然后把离散整变量连续化，从而非线性混合整数规划化为与之等价的无约束非线性规划。本文弱化了文[6]中定理1的条件，并得到了相应的结论。     

函数的C-拟凸性

给出了在存在t0∈(0,1)满足f(t0x1 (1-t0)x2)∈y-C,for y∈E,f(x1),f(x2)∈y-C,的条件下函数f具有C-拟凸性的充分必要条件和一些相应的结果。     

凹资源配置问题的混合动态规划方法

Concave resource allocation problem is an integer programming problem of minimizing a nonincreasing concave function subject to a convex nondecreasing constraint and bounded integer variables. This class of problems are encountered in optimization models involving economies of scale. In this paper, a new hybrid dynamic programming method was proposed for solving concave resource allocation problems. A convex underestimating function was used to approximate the objective function and the resulting convex subproblem was solved with dynamic programming technique after transforming it into a 0-1 linear knapsack problem. To ensure the convergence, monotonicity and domain cut technique was employed to remove certain integer boxes and partition the revised domain into a union of integer boxes. Computational results were given to show the efficiency of the algorithm.     

包含r-invex函数的连续时间最优化问题

Antczak提出了一类非凸的可微函数并将其称为r-invex函数,它是invex函数的一种推广。论文定义了一类KKT-r-invex函数,讨论了该类函数的一些性质,并将其应用到连续时间非线性最优化问题(CNP)中,从而获得了Karush-Kuhn-Tucker点是全局最优解的一个充分必要条件。论文的主要结果推广了已有的相应结果。     

广义凸规划问题的最优性条件

B—预凸函数是一类广义凸函数,该文推广了B—预凸函数的定义,给出了一类新的函数B—致凸函数的定义,在约束函数和目标函数都是B—致凸的条件下讨论了一类可微多目标规划的最优性条件,其结论具有一般性,推广了许多文献中关于B—预凸函数的结果。     

线性规划问题的最优解的广义逆矩阵理论

文中利用广义逆矩阵研究线性规划问题,并给出了线性规划问题与线性不等式组的关系,简洁地证明了在广义逆矩阵下线性规划问题有最优解的一些充要条件以及在广义逆矩阵下的对偶定理,为研究线性规划问题的解提供了一种新方法。     

连通图的一种简单判别法

利用代数方法,给出无向图为连通图的充分必要条件,进一步得到判别“0—1”正线对称矩阵可幺化的简便方法。     

完全二部图的P5—因子分解

本文给出了完全二部图的P5-因子分解存在的必要条件,同时讨论了充分条件的几种情况,给出了四个猜想。     

S—分离性与R—分离性

本文首先给出S_i—空间(i=0,1,2)的若干等价条件,然后定义另一种分离性:R—分离性并讨论其性质。     

企业资产结构优化的宏观分析及对策

合理的资产结构是企业正常经营并实现良性循环的必要条件.我国企业目前资产结构不尽合理,严重威胁着企业的生存与发展,对整个国民经济的发展也产生了极为不利的影响.本文对我国企业的资产结构的现状、问题及成因从宏观层面上进行了深入分析,在此基础上,从我国的实际出发,提出了优化我国企业资产结构的宏观对策.     

一类双重退化的奇异扩散方程

根据YIN和WANG的方法,结合Fichera-Oleinik理论,研究奇异扩散方程：φ（ u）/t =div（ραu p-2u）,（x,t）∈QT =Ωx（0,T）,其中Ω是RN 中的有界区域,边界Ω充分光滑,ρ（x）=dist（x,Ω）, p 〉1,α〉0,φ满足：φ∈C2,且存在δ〉0使得φ′（s）〉δ〉0.证明了α≥p -1时,不需要任何边值条件,方程最多有一个满足初值条件的解;而0〈α〈 p -1时,方程存在唯一满足初边值条件弱解.     

民族地区社会经济发展与职业教育体系的构建

现代意义上的职业教育,实际上是一种狭义的就业前的技能培训。但作为教育体系的确立,需要完备的支撑条件,其职业教育的运行才能够显示其生命力。学校义务教育与劳务市场的形成是建构我国职业教育的必要前提,而其技术设备的更新、行业结构的改组和市场信息的快速传递与反馈等因素就构成了我国职业教育的充要条件。这些要素乃是构建职业教育体系应当具备的不可或缺的条件。     

Visual environment and delay affect cache retrieval accuracy in a food-storing rodent

Many scatter-hoarding species use spatial memory to relocate their food caches. Two factors can affect spatial memory: the availability of landmarks in the environment, and the latency between learning and recall. Using a 2 × 2 factorial design, we determined the effect of these factors on cache retrieval accuracy in Merriam’s kangaroo rats (Dipodomys merriami). Kangaroo rats cached seeds in an arena under conditions that varied by retrieval interval (1 or 10 days) and by number of landmarks (0 or 16 landmarks). After 1 day, they recovered equal proportions of caches in both landmark conditions. After 10 days, they recovered more caches in the 16-landmark condition than in the bare condition. This is the first study to show that landmarks are necessary for accurate cache recovery after long delays. This result is consistent with maze studies that have shown that landmarks reduce proactive interference and that delay increases proactive interference.     

Algorithms,Visualization, and Mental Models: High School Students' Interactions with a Relative Motion Simulation

Galileo's contemporaries as well as today's students have difficulty understanding relative motion. We hypothesize that the construction of visual models, resolution of these visual models with numeric models, and, in many cases, rejection of commitments such as the belief in one true velocity, are necessary for students to form integrated mental models of relative motion events. To investigate students' relative motion problem solving, high school science students were videotaped in classroom and laboratory settings as they performed collaborative predict-observe-explain activities with relative motion computer simulations. Half of the students interacted with simulations that provided animated feedback; the other half received numeric feedback. Learning, as measured by a diagnostic test, occurred following both conditions. There is evidence that many numeric condition students used faulty mechanical algorithms to solve problems, while many animation condition students used mental imagery to solve problems. In this paper, interactions in which student involvement was visual model based will be contrasted with interactions in which involvement was algorithm based. Implications for pedagogy and educational uses of computer simulations will be discussed.