Generalized Surrogate Problem Methodology for Online Stochastic Discrete Optimization

We consider stochastic discrete optimization problems where the decision variables are nonnegative integers and propose a generalized surrogate problem methodology that modifies and extends previous work in Ref. 1. Our approach is based on an online control scheme which transforms the problem into a surrogate continuous optimization problem and proceeds to solve the latter using standard gradient-based approaches while simultaneously updating both the actual and surrogate system states. In contrast to Ref. 1, the proposed methodology applies to arbitrary constraint sets. It is shown that, under certain conditions, the solution of the original problem is recovered from the optimal surrogate state. Applications of this approach include solutions to multicommodity resource allocation problems; in these problems, exploiting the convergence speed of the method, one can overcome the obstacle posed by the presence of local optima.     

Relaxation-based algorithms for minimax optimization problems with resource allocation applications

We consider minimax optimization problems where each term in the objective function is a continuous, strictly decreasing function of a single variable and the constraints are linear. We develop relaxation-based algorithms to solve such problems. At each iteration, a relaxed minimax problem is solved, providing either an optimal solution or a better lower bound. We develop a general methodology for such relaxation schemes for the minimax optimization problem. The feasibility tests and formulation of subsequent relaxed problems can be done by using Phase I of the Simplex method and the Farkas multipliers provided by the final Simplex tableau when the corresponding problem is infeasible. Such relaxation-based algorithms are particularly attractive when the minimax optimization problem exhibits additional structure. We explore special structures for which the relaxed problem is formulated as a minimax problem with knapsack type constraints; efficient algorithms exist to solve such problems. The relaxation schemes are also adapted to solve certain resource allocation problems with substitutable resources. There, instead of Phase I of the Simplex method, a max-flow algorithm is used to test feasibility and formulate new relaxed problems.Corresponding author.Work was partially done while visiting AT&T Bell Laboratories.     

Buffer allocation for a class of nonlinear stochastic knapsack problems

In this paper, we examine a class of nonlinear, stochastic knapsack problems which occur in manufacturing, facility or other network design applications.Series, merge-and-split topologies of series-parallelM/M/1/K andM/M/C/K queueing networks with an overall buffer constraint bound are examined. Bounds on the objective function are proposed and a sensitivity analysis is utilized to quantify the effects of buffer variations on network performance measures.     

利用相位共轭与色散配置实现具有大占空比和大放大器间隔的长距离光孤子传输

在用光纤放大器补偿损耗的光纤传输线中，用负色散光纤与正色散光纤或色散补偿器件交叉配置，并使传输线中光纤的有效色散适当大于（与平均孤子对应的）理论值，同时在传输线中周期地使用相位共轭器，可以在把放大器间隔提高到与常规光纤通信相同的条件下有效地削弱孤子之间的互作用。本文对实现速率为２５Ｇｂｉｔ／ｓ、占空比为１／２、光放大器间隔为１００ｋｍ、传输距离大于６０００ｋｍ的光孤子传输作出了数值论证     

对民事诉讼回避制度的思考

回避制度对案件能否公正审判有重要意义，我国现行回避制度尚有诸多不足之处，当事人对审判人员能否公正执法产生合理怀疑也应可提请回避。     

小型电缆电视传输系统设计方法

本文从信号分配和前端设备配置两方面,介绍了小型电缆电视多路传输系统的设计方法。该方法以一个实例为线索,其信号分配灵活多样,既反映了系统设计的一般方法,又体现了小型系统简便易行的设计特点,因而,对设想安装小型电缆电视系统的单位具有参考价值。同时,该方法也可作为小型共用天线电视系统的设计参考。     

钢铁厂煤气资源的最优分配

建立了钢铁厂煤气资源旬计划最优分配模型,利用替代松弛法可以在微机上迅速求解这个0—1整数规划模型。仿真说明,用本模型可以显著改进煤气资源的分配,减少煤气放散,提高经济效益。     

一种二次循环多目标规划可行性研究方法

本文是以资源开发利用、企业革新改造项目为背景,运用系统工程、模糊数学方 法,提出了一种二次循环多目标规划进行可行性研究方法,建立了一套项目系统模 型。本方法运用于某天然气资源的开发利用项目,获得了满意的结果．     

Power allocation for cognitive underlay networks with spectrum band selection

In this paper, we study the cooperative communication of a cognitive underlay network by utilizing the diversity of multiple spectrum bands. In particular, we assume that the transmission power of the secondary user (SU) is subject to different joint constraints, such as peak interference power of the multiple primary users (PUs), peak transmission power of the SU, outage tolerate interference, and outage probability threshold. Accordingly, two power allocation schemes are considered on the basis of the minimum interference channel from the SU to the PU and the channel state information of the primary user link. Furthermore, the SU can select one of the three transmission modes following the channel state conditions, namely as cellular, device-to-device, or switching mode, to transmit the signal to the secondary user receiver. Given this setting, two power allocation schemes over a spectrum band selection strategy are derived. In addition, closed-form expressions for the outage probability of three modes are also obtained to evaluate the performance of the secondary network. Most importantly, a closed-form expression for the peak interference power level of the PU, which is considered as one of the most important parameters to control the SU’s transmission power, is derived by investigating the relation of two considered power allocation schemes in the practise. Finally, numerical examples show that the outage performance of secondary network in the switching mode outperforms the one of the cellular and device-to-device (D2D) mode for all considered power allocation schemes.     

Extremes for coherent risk measures

Various concepts appeared in the existing literature to evaluate the risk exposure of a financial or insurance firm/subsidiary/line of business due to the occurrence of some extreme scenarios. Many of those concepts, such as Marginal Expected Shortfall or Tail Conditional Expectation, are simply some conditional expectations that evaluate the risk in adverse scenarios and are useful for signaling to a decision-maker the poor performance of its risk portfolio or to identify which sub-portfolio is likely to exhibit a massive downside risk. We investigate the latter risk under the assumption that it is measured via a coherent risk measure, which obviously generalizes the idea of only taking the expectation of the downside risk. Multiple examples are given and our numerical illustrations show how the asymptotic approximations can be used in the capital allocation exercise. We have concluded that the expectation of the downside risk does not fairly take into account the individual risk contribution when allocating the VaR-based regulatory capital, and thus, more conservative risk measurements are recommended. Finally, we have found that more conservative risk measurements do not improve the fairness of the cost of capital allocation when the uncertainty with parameter estimation is present, even at a very high level.