共查询到19条相似文献,搜索用时 218 毫秒
1.
加权 l1最小化是稀疏优化的主流方法之一。本文对带非负约束的 l0最小化问题与加权 l1最小化问题的解之间的关系进行了研究,给出了加权 l1最小化问题的约束矩阵和目标函数的系数是" s-权优"的定义,并通过该定义给出了加权 l1最小化问题的解是带非负约束的 l0最小化问题的解的条件。进一步,本文给出了" s-权优"的充分条件及其具体表示形式,并对其上下界进行了可计算的有效估计。 相似文献
2.
G是一个 k-连通图, T是 G的一个 k-点割,若 G- T可被划分成两个子图 G1, G2,且| G1|≥2,| G2|≥2,则称 T是 G的一个非平凡点割。假定 G是一个不含非平凡( k-1)点割的( k-1)-连通图,则称 G是一个拟 k-连通图。证明了对任意一个 k≥5且 t> $ \frac{k}{2}$的整数,若 G是一个不含( K2+ tK1)的 k-连通图,且 G中任意两个不同点对 v, w,有 d( v)+ d( w)≥ $\frac{{3k}}{2} $+ t,则对 G中的任意一个点,存在一条与之关联的边收缩后可以得到一个拟 k-连通图,且 G中至少有 $\frac{{\left| {V\left( G \right)} \right|}}{2} $条边使得收缩其中任意一条边后仍是拟 k-连通的。 相似文献
3.
本文研究了在边界和算子摄动相结合的情况下高阶椭圆型方程解的渐近式的构造.如果非摄动问题A 0不在谱上,则摄动问题A ε的渐近解可按小参数ε的次幂展开;如果A 0在谱上,则在A ε的渐近解中出现有小参数ε的负幂;同时给出了有关的余项的估计. 相似文献
4.
给定两个非负整数 s和 t,图 G的( s, t)-松弛强 k边着色可表示为映射 c: E( G)→[ k],这个映射满足对 G中的任意一条边 e,颜色 c( e)在 e的1-邻域中最多出现 s次并且在 e的2-邻域中最多出现 t次。图 G的( s, t)-松弛强边着色指数,记作 χ' (s,t)( G),表示使得图 G有( s, t)-松弛强 k边着色的最小 k值。在图 G中,如果mad( G) < 3并且Δ≤4,那么 χ' (1,0)( G)≤3Δ。并证明如果 G是平面图,最大度Δ≥4并且围长最少为7,那么 χ' (1,0)( G)≤3Δ-1。 相似文献
5.
假设 G=( V, E, F)是一个平面图。如果 e1和 e2是 G中两条相邻边且在关联的面的边界上连续出现,那么称 e1和 e2面相邻。图 G的一个弱完备 k-染色是指存在一个从 V ∪ E ∪ F到 k色集合{1, …, K}的映射,使得任意两个相邻点,两个相邻面,两条面相邻的边,以及 V ∪ E ∪ F中任意两个相关联的元素都染不同的颜色。若图 G有一个弱完备 k-染色,则称 G是弱完备 k-可染的。平面图 G的弱完备色数是指 G是弱完备 k-可染的正整数 k的最小值,记成 χvef( G)。2016年,Fabrici等人猜想:每个无环且无割边的连通平面图是弱完备7-可染的。证明外平面图满足猜想,即外平面图是弱完备7-可染的。 相似文献
6.
通过马氏链拟合的方法求取一种新的非负时变权组合预测算法公式.主要工作是:一、对组合预测问题以最小误差为准则给出了马氏链的状态和状态概率初步估计;二、用马氏链拟合状态概率分布时变规律,通过约束多元自回归模型导出了一步转移概率阵的LS解;三、给出一种非负时变权组合预测公式并举一应用实例. 相似文献
7.
通过研究单位L ∞范数下的带值约束的最大权完美匹配逆问题的性质,将单位L ∞范数下最大权完美匹配逆问题转化为求解最大平均交替圈问题,给出一个求解该类问题的一个强多项式时间算法,其时间复杂度为O(n 4).并通过一个算例,验证了给出的算法的有效性. 相似文献
8.
对任意区间[t 0,t 1]任意初值为x 0和终值为x 1的Brown桥,即随机微分方程dx=(x 1-x)/(t 1-t)dt+dB(t) x(t 0)=x 0,给出其解析解(包括随机积分解和Fourier级数解),及Milstein数值解并进行期望和方差分析,求得期望函数、期望±标准差曲线和95%置信区间边界曲线.并对不同Brown运动对应的不同轨线实现进行仿真模拟.对一个非真实的近似解加以辨别. 相似文献
9.
基于重大事故规避的思想,建立以最大事故后果最小及运输成本最小为双目标,且事故后果基于实时装载量的危险品运输车辆路径优化模型。基于 ε-约束法,设计可求得帕累托最优解的精确算法,该算法包含通过性质求 ε下界、规避被支配解的预处理及不可行路径禁止约束3处改进。进一步设计处理大规模问题的多项式时间近似算法,并分析了算法的近似比。最后通过算例对模型和算法进行测试,并通过出灵敏度分析给出管理启示。 相似文献
10.
该文研究了一类具有非局部效应和非线性发生率的时滞SEIR系统的周期行波解.首先,定义基本再生数R 0并构造适当的上下解,将周期行波解的存在性转化为闭凸集上非单调算子的不动点问题,利用Schauder不动点定理结合极限理论建立该系统周期行波解的存在性.其次,利用反证法结合比较原理,建立当基本再生数R 0<1时该系统周期行波解的不存在性. 相似文献
11.
The following problem is considered: given: an undirected planar graph G=( V, E) embedded in
, distinct pairs of vertices { r1, s1},…,{ rk, sk} of G adjacent to the unbounded face, positive integers b1,…, bk and a function
; find: pairwise vertex-disjoint paths P1,…, Pk such that for each i=1,…, k, Pi is a ri− si-path and the sum of the l-length of all edges in Pi is at most bi. It is shown that the problem is NP-hard in the strong sense. A pseudo-polynomial-time algorithm is given for the case of k=2. 相似文献
12.
We consider a variation of a classical Turán-type extremal problem (F. Chung, R. Graham, Erd
s on Graphs: His Legacy of Unsolved Problems, AK Peters Ltd., Wellesley, 1998, Chapter 3) as follows: Determine the smallest even integer σ( Kr,s, n) such that every n-term graphic sequence π=( d1, d2,…, dn) with term sum σ(π)= d1+ d2++ dnσ( Kr,s, n) is potentially Kr,s-graphic, where Kr,s is a r× s complete bipartite graph, i.e., π has a realization G containing Kr,s as its subgraph. In this paper, we first give sufficient conditions for a graphic sequence being potentially Kr,s-graphic, and then we determine σ( Kr,r, n) for r=3,4. 相似文献
13.
For a 1-dependent stationary sequence { Xn} we first show that if u satisfies p1= p1( u)= P( X1> u)0.025 and n>3 is such that 88 np131, then P{max(X1,…,Xn)u}=ν·μn+O{p13(88n(1+124np13)+561)}, n>3, where ν=1−p2+2p3−3p4+p12+6p22−6p1p2,μ=(1+p1−p2+p3−p4+2p12+3p22−5p1p2)−1 with pk=pk(u)=P{min(X1,…,Xk)>u}, k1 and From this result we deduce, for a stationary T-dependent process with a.s. continuous path { Ys}, a similar, in terms of P{max 0skTYs< u}, k=1,2 formula for P{max 0stYsu}, t>3 T and apply this formula to the process Ys= W( s+1)− W( s), s0, where { W( s)} is the Wiener process. We then obtain numerical estimations of the above probabilities. 相似文献
14.
逻辑回归是经典的分类方法,广泛应用于数据挖掘、机器学习和计算机视觉.现研究带有程。模约束的逻辑回归问题.这类问题广泛用于分类问题中的特征提取,且一般是NP-难的.为了求解这类问题,提出了嵌套BB(Barzilai and Borwein)算法的分裂增广拉格朗日算法(SALM-BB).该算法在迭代中交替地求解一个无约束凸优化问题和一个带程。模约束的二次优化问题.然后借助BB算法求解无约束凸优化问题.通过简单的等价变形直接得到带程。模约束二次优化问题的精确解,并且给出了算法的收敛性定理.最后通过数值实验来测试SALM-BB算法对稀疏逻辑回归问题的计算精确性.数据来源包括真实的UCI数据和模拟数据.数值实验表明,相对于一阶算法SLEP,SALM-BB能够得到更低的平均逻辑损失和错分率. 相似文献
15.
Let sk( n) be the largest integer such that every n-point interval order with no antichain of more than k points includes an sk( n)-point semiorder. When k = 1, s1( n) = n since all interval orders with no two-point antichains are chains. Given ( c1,..., c5) = (1, 2, 3, 4), it is shown that s2( n) = cn for n 4, s3( n) = cn for n 5, and for all positive n, s2 ( n+4) = s2( n)+3, s3( n+5) = s3( n)+3. Hence s2 has a repeating pattern of length 4 [1, 2, 3, 3; 4, 5, 6, 6; 7, 8, 9, 9;...], and s3 has a repeating pattern of length 5 [1, 2, 3, 3, 4; 4, 5, 6, 6, 7; 7, 8, 9, 9, 10;...]. Let s(n) be the largest integer such that every n-point interval order includes an s(n)-point semiorder. It was proved previously that
for even n from 4 to 14, and that s(17) = 9. We prove here that s(15) = s(16) = 9, so that s begins 1, 2, 3, 3, 4, 4,..., 8, 8, 9, 9, 9. Since s(n)/n→0, s cannot have a repeating pattern. 相似文献
16.
Let S be a compact, weak self-similar perfect set based on a system of weak contractions fj, j=1,…, m each of which is characterized by a variable contraction coefficient j( l) as d( fj( x), fj( y)) j( l) d( x, y), d( x, y)< l, l>0. If the relation ∑ mj=1j( l0)<1 holds at at least one point l0, then every nonempty compact metric space is a continuous image of the set S. 相似文献
17.
Let X1, X2,…be identically distributed random variables from an unknown continuous distribution. Further let Ir(1), Ir(2),…be a sequence of indicator functions defined on X1, X2,…by Ir( k) = 0 if k < r, Ir( k) = 1 if Xk is a r-record AND = 0 otherwise. Suppose that we observe X1, X2,… at times T1 < T2 <… where the Tk's are realisations of some regular counting process ( N(τ)) defined on the positive half-line. Having observed [0, τ], say, the problem is to predict the future behaviour of the counting processes ( Rr(τ, s)) sτ = # r-records in [τ, s]. More specifically the objective of this paper is to show that these processes can be (inhomogeneous) Poisson processes even if ( N(τ)) τ0 has dependent increments. The strong link between optimal selection and optimal stopping of record sequences or record processes, perhaps not fully recognized so far, is pointed out in this paper. It is shown to lead to a unification of the treatment of problems which, at first sight, are rather different. Moreover the stopping of record processes in continuous time can lead to rigorous and elegant solutions in cases where dynamic programming is bound to fail. Several examples will be given to facilitate a comparison with other methods. 相似文献
18.
We study the asymptotic behaviour of the occupation time process ∫ t0 IA( W1( L2( s)))d s, t 0, where W1 is a standard Wiener process and L2 is a Wiener local time process at zero that is independent from W1. We prove limit laws, as well as almost sure upper and lower class theorems. Possible extensions of the obtained results are also discussed. 相似文献
19.
Let I be a compact interval of real axis R, and(I, H) be the metric space of all nonempty closed subintervals of I with the Hausdorff metric H and f : I → I be a continuous multi-valued map. Assume that Pn =(x_0, x_1,..., xn) is a return tra jectory of f and that p ∈ [min Pn, max Pn] with p ∈ f(p). In this paper, we show that if there exist k(≥ 1) centripetal point pairs of f(relative to p)in {(x_i; x_i+1) : 0 ≤ i ≤ n-1} and n = sk + r(0 ≤ r ≤ k-1), then f has an R-periodic orbit, where R = s + 1 if s is even, and R = s if s is odd and r = 0, and R = s + 2 if s is odd and r 0. Besides,we also study stability of periodic orbits of continuous multi-valued maps from I to I. 相似文献
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