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最近,Zhao和Sun提出了一个求解sufficient线性互补问题的高阶不可行内点算法.不需要严格互补解条件,他们的算法获得了高阶局部收敛率,但他们的文章没有报告多项式复杂性结果.本文我们考虑他们所给算法的一个简化版本,即考虑求解单调水平线性互补问题的一个高阶可行内点算法.我们证明了算法的迭代复杂性是 相似文献
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本文通过使用相同的矩阵因子,给出了一个求解单调线性互补问题的r-阶Mehrotra型宽城不可行内点算法,其中嵌入Wright的快速步与安全步算法.所给算法的迭代复杂性为O(n~((r 1)/r)L).在考虑的问题有一个严格互补解的条件下,所给算法具有2阶Q-超线性收敛性. 相似文献
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在(2)中,Harker和Pang提出了如下一个公开问题,对于线性互补问题的阻尼牛顿算法,当它收敛时,算法是否能在有限步内终止?本文对此问题给出一个肯定回答,而且进一步给出一个新的求解一般线性互补问题的有限终止算法,这个算法避免了阻尼牛顿算法可能不收敛的情形。 相似文献
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考虑广义线性互补问题,提出一个求解它的改进的序列线性规划算法,并在一定条件下证得该法具有良好的收敛性质。此外,顺便给出该问题解集非空有界的一个充分条件。 相似文献
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本文基于一个带参数的函数,为P*(κ)线性互补问题设计出了一个大步校正内点算法.算法讨论沿用了Peng等在文[9]对互补问题基于自正则函数的讨论模式.但是,与Peng的算法不同的是,我们所考虑的带参数的函数是非自正则的.算法最终被证明具有较好的多项式复杂性. 相似文献
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首先将一个具有多个约束的规划问题转化为一个只有一个约束的规划问题,然后通过利用这个单约束的规划问题,对原来的多约束规划问题提出了一些凸化、凹化的方法,这样这些多约束的规划问题可以被转化为一些凹规划、反凸规划问题.最后,还证明了得到的凹规划和反凸规划的全局最优解就是原问题的近似全局最优解. 相似文献
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该文研究三种新变形的全一问题及最小全一问题. 原始的全一问题可被形象的称为顶点点亮顶点问题, 而这三类新问题则分别被称为顶点点亮边问题,边点亮顶点问题,边点亮边问题. 顶点点亮顶点问题已经得到了广泛的研究. 比如,解的存在性问题和求解的有效算法已经被解决,一般图上的最小顶点点亮顶点问题已经被证明是NP- 完备的,树、单圈图和双圈图上的最小顶点点亮顶点问题的线性时间最优算法也已被给出等. 该文对于顶点点亮边问题,证明一个图有解当且仅当它是二部图,因此只可能有两组解和最优解. 对于边点亮顶点问题,证明一个图有解当且仅当它包含偶数个顶点,并通过将其最优问题多项式变换成最小权的完美匹配问题,得出一般图上的最小边点亮顶点问题可在多项式时间内求解. 边点亮边问题可归约成线图上的顶点点亮顶点问题. 相似文献
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下层问题以上层决策变量作为参数,而上层是以下层问题的最优值作为响应
的一类最优化问题——二层规划问题。我们给出了由一系列此类二层规划去逼近原二层规划的逼近法,得到了这种逼近的一些有趣的结果. 相似文献
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Richard L. Francis Gordon P. Wright 《Journal of Optimization Theory and Applications》1969,4(6):394-412
In 1963, Kuhn presented a dual problem to a relatively well-known location problem, variously referred to as the generalized Fermat problem and the Steiner-Weber problem. The purpose of this paper is to point out how Kuhn's results can be adapted to provide a dual to the generalized Neyman-Pearson problem, a problem of fundamental interest in statistics, which has applications in control theory and a number of other areas. The Neyman-Pearson problem, termed the dual problem, is a constrained maximization problem and may be considered to be a calculus-of-variations analog to the bounded-variable problem of linear programming. When the dual problem has equality constraints, the primal problem is an unconstrained minimization problem. Duality results are also obtained for the case where the dual problem has inequality constraints.This work was partially supported by the National Science Foundation, Grant Nos. NSF-GK-1571 and NSF-GK-3038. The authors would like to acknowledge the very useful comments of one of the referees, which led to more direct and general proofs of Properties 2.3 and 2.6. 相似文献
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《Operations Research Letters》2023,51(1):84-91
In this paper, we study the bilevel programming problem with discrete polynomial lower level problem. We start by transforming the problem into a bilevel problem comprising a semidefinite program (SDP for short) in the lower level problem. Then, we are able to deduce some conditions of existence of solutions for the original problem. After that, we again change the bilevel problem with SDP in the lower level problem into a semi-infinite program. With the aid of the exchange technique, for simple bilevel programs, an algorithm for computing a global optimal solution is suggested, the convergence is shown, and a numerical example is given. 相似文献
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The complexity status of Pendants-median spanning tree problem is an open problem. Using the complexity of the X3C problem, the paper proves that Pendants-median spanning tree problem is NP-complete. Global-median spanning tree problem is a related problem. Using the complexity of 3SAT, the paper proves that this problem is also NP-complete, and a polynomial -time algorithm to this problem is given, whose time complexity is O(n^3). 相似文献
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现代物流技术中装卸工问题的拟多项式时间可解情况 总被引:10,自引:0,他引:10
装卸工问题是从现代物流技术中提出的一个实际问题,这个问题的雏形早在上个世纪60年代中国科学院数学研究所就提出和研究过。现代物流业的迅速发展,促成和推动装卸工问题的提出和研究。装卸工问题是一个新的NP困难的组合优化问题,本文研究限制情形下的装卸工问题,并证明是拟多项式时间可解的。 相似文献
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The zero-one knapsack problem is a linear zero-one programming problem with a single inequality constraint. This problem has been extensively studied and many applications and efficient algorithms have been published. In this paper we consider a similar problem, one with an equality instead of the inequality constraint. By replacing the equality by two inequalities one of which is placed in the economic function, a Lagrangean relaxation of the problem is obtained. The relation between the relaxed problem and the original problem is examined and it is shown how the optimal value of the relaxed problem varies with increasing values of the Lagrangean multiplier. Using these results an algorithm for solving the problem is proposed.The paper concludes with a discussion of computational experience. 相似文献
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A general continuous review production planning problem with stochastic demand is considered. Conditions under which the stochastic problem may be correctly solved using an equivalent deterministic problem are developed. This deterministic problem is known to have the same solution as the stochastic problem. Moreover, conditions are established under which the deterministic equivalent problem differs from a commonly used deterministic approximation to the problem only in the interest rate used in discounting. Thus, solving the stochastic problem is no more difficult than solving a commonly used approximation of the problem. 相似文献
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装卸工问题是从现代物流技术中提出的一个实际问题,这个问题的雏形早在上个世纪60年代中国科学院数学研究所就提出和研究过.现代物流技术迅速发展,促成和推动装卸工问题的提出和研究.装卸工问题是一个新的NP困难的组合优化问题,首先介绍装卸工问题及限制情况下装卸工问题的数学模型,然后分析限制情况下的装卸工问题的性质,最后给出该问题的所有最优解. 相似文献