Concave minimization over a convex polyhedron

A general algorithm is developed for minimizing a well defined concave function over a convex polyhedron. The algorithm is basically a branch and bound technique which utilizes a special cutting plane procedure to' identify the global minimum extreme point of the convex polyhedron. The indicated cutting plane method is based on Glover's general theory for constructing legitimate cuts to identify certain points in a given convex polyhedron. It is shown that the crux of the algorithm is the development of a linear undrestimator for the constrained concave objective function. Applications of the algorithm to the fixed-charge problem, the separable concave programming problem, the quadratic problem, and the 0-1 mixed integer problem are discussed. Computer results for the fixed-charge problem are also presented.     

Properties of a mean residual life function arising from renewal theory

The present article discusses the properties of the mean residual life function in a renewal process. We examine the relationship this function has with the failure rate function and the conventional mean, variance and coefficient of variation of residual life. We also discuss some monotonicity properties of the mean residual life function. A partial order based on the renewal mean residual function is introduced along with its interrelationship with some existing stochastic orders. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

A finite descent theory for linear programming,piecewise linear convex minimization,and the linear complementarity problem

A descent algorithm simultaneously capable of solving linear programming, piecewise linear convex minimization, and the linear complementarity problem is developed. Conditions are given under which a solution can be found in a finite number of iterations using the geometry of the problem. A computer algorithm is developed and test problems are solved by both this method and Lemke's algorithm. Current results indicate a decrease in the number of cells visited but an increase in the total number of pivots needed to solve the problem.     

On the theory of semi-infinite programming and a generalization of the kuhn-tucker saddle point theorem for arbitrary convex functions

We first present a survey on the theory of semi-infinite programming as a generalization of linear programming and convex duality theory. By the pairing of a finite dimensional vector space over an arbitrarily ordered field with a generalized finite sequence space, the major theorems of linear programming are generalized. When applied to Euclidean spaces, semi-infinite programming theory yields a dual theorem associating as dual problems minimization of an arbitrary convex function over an arbitrary convex set in n-space with maximization of a linear function in non-negative variables of a generalized finite sequence space subject to a finite system of linear equations. We then present a new generalization of the Kuhn-Tucker saddle-point equivalence theorem for arbitrary convex functions in n-space where differentiability is no longer assumed.     

Maximizing the ratio of two convex functions over a convex set

The purpose of this article is to present an algorithm for globally maximizing the ratio of two convex functions f and g over a convex set X. To our knowledge, this is the first algorithm to be proposed for globally solving this problem. The algorithm uses a branch and bound search to guarantee that a global optimal solution is found. While it does not require the functions f and g to be differentiable, it does require that subgradients of g can be calculated efficiently. The main computational effort of the algorithm involves solving a sequence of subproblems that can be solved by convex programming methods. When X is polyhedral, these subproblems can be solved by linear programming procedures. Because of these properties, the algorithm offers a potentially attractive means for globally maximizing ratios of convex functions over convex sets. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

Minimizing the makespan in open‐shop scheduling problems with a convex resource consumption function

We consider open‐shop scheduling problems where operation‐processing times are a convex decreasing function of a common limited nonrenewable resource. The scheduler's objective is to determine the optimal job sequence on each machine and the optimal resource allocation for each operation in order to minimize the makespan. We prove that this problem is NP‐hard, but for the special case of the two‐machine problem we provide an efficient optimization algorithm. We also provide a fully polynomial approximation scheme for solving the preemptive case. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

Maximum matching in a convex bipartite graph

A special matching problem arising in industry is shown to be solvable by an algorithm of the form: match objects a_i and b_j if they satisfy a local optirnality criterion based on a ranking of currently unmatched objects. When no a_i and b_i remain that can be matched, the largest number of acceptable matches has been found.     

西方市场失灵理论评析

市场经济并不是完美无缺的。市场失灵会影响到社会发展目标的实现和资源的有效配置。对此 ,西方经济学家提出了一系列理论观点。这些理论分析对建立社会主义市场经济体制具有借鉴意义。     

On maximization of the integral of a bell-shaped function over a symmetric set

Given a target T in Euclidean n-space Rⁿ and a point bomb whose point of impact in Rⁿ is governed by a probability distribution about the aim point a, what choice of a maximizes the probability of a hit v_a(T)? Of course, only in special cases is an exact solution of this problem obtainable. This paper treats targets T which are symmetric about the origin o and demonstrates conditions on the extent of T and the impact density f, a density with respect to Lebesgue measure, sufficient for v_a(T) to be monotone in the distance from a to o and maximized at a = o. The results are applied to various tactical situations.     

On convexity proofs in location theory

It is often assumed in the facility location literature that functions of the type ø_i(x_i, y) = β_i[(x_i-x)²+(y_i-y)²]^K/2 are twice differentiable. Here we point out that this is true only for certain values of K. Convexity proofs that are independent of the value of K are given.     

当代社会剩余价值分配理论探析

传统的剩余价值分配理论认为,雇佣劳动者创造的全部剩余价值被资产阶级所独占,这符合资本主义发展初期的客观实际。伴随社会生产力的不断发展,当代社会剩余价值的分配发生了新的变化。雇佣劳动者创造的剩余价值不再被资本所有者所独占,而是以不同的方式被投入各种要素的不同所有者以不同的方式所拥有。     

劳动价值论科学内涵探析

进一步界定劳动价值论的科学内涵 ,是坚持、丰富和发展马克思主义劳动价值论的需要 ,是“新的实际”的需要。只有坚持并正确理解马克思主义劳动价值一元论 ,准确扩展生产劳动概念 ,科学界定、正确认识服务劳动、管理劳动、科技劳动等在价值创造中的重要地位和独特作用 ,才能丰富和发展马克思主义劳动价值论的科学内涵。     

图书馆社会导向功能浅论

图书馆主要从事吸纳、处理、发送信息资料的过程性活动。由于其所操控的信息资料量大 ,因而在其过程性活动中必然对社会具有导向作用。充分认识并发挥图书馆的社会导向功能 ,对推进社会主义现代化建设 ,尤其是精神文明建设具有重要意义 ,对准确定位新时期图书馆工作、充分发挥其作用也有重要意义。     

Some distributions arising as a consequence of errors in inspection

In this article, the authors survey and consolidate their investigations during the years 1980-1983 dealing with consequences of errors in inspection sampling models. Some indication of the current and future research is given.     

论火灾形成的认识论基础

立足减少火灾对人类的危害 ,从哲学的视角剖析火灾形成的认识论基础。主要从自然观、人类实践行为、人的消费观念及价值取向进行全面论述 ,揭示当代火灾形成的直接原因、社会因素和思想根源。     

Application of Markov renewal theory and semi-Markov decision processes in maintenance modeling and optimization of multi-unit systems

In this paper, a condition-based maintenance model for a multi-unit production system is proposed and analyzed using Markov renewal theory. The units of the system are subject to gradual deterioration, and the gradual deterioration process of each unit is described by a three-state continuous time homogeneous Markov chain with two working states and a failure state. The production rate of the system is influenced by the deterioration process and the demand is constant. The states of the units are observable through regular inspections and the decision to perform maintenance depends on the number of units in each state. The objective is to obtain the steady-state characteristics and the formula for the long-run average cost for the controlled system. The optimal policy is obtained using a dynamic programming algorithm. The result is validated using a semi-Markov decision process formulation and the policy iteration algorithm. Moreover, an analytical expression is obtained for the calculation of the mean time to initiate maintenance using the first passage time theory.     

论知识移植在量子力学发展过程中的作用

从量子力学的形成和发展过程可以看到知识移植对物理学的发展起到了巨大的推动作用,通过知识移植不仅能够实现创新,甚至可能导致科学的重大发现。如何在教学活动中通过对科学史的总结和归纳来引导学生形成创新意识在当前我国的大学教育必须加以关注。     

论江泽民保持社会思想稳定理论

江泽民思想稳定理论继承和发展了邓小平稳定理论。其主要内容是 :科学概括了保持社会思想稳定的重要性 ,形成了社会主义意识形态理论的新特色 ,要高度重视社会舆论工作。