Characterizing global optimality for DC optimization problems under convex inequality constraints

Characterizations of global optimality are given for general difference convex (DC) optimization problems involving convex inequality constraints. These results are obtained in terms of -subdifferentials of the objective and constraint functions and do not require any regularity condition. An extension of Farkas' lemma is obtained for inequality systems involving convex functions and is used to establish necessary and sufficient optimality conditions. As applications, optimality conditions are also given for weakly convex programming problems, convex maximization problems and for fractional programming problems.This paper was presented at the Optimization Miniconference held at the University of Ballarat, Victoria, Australia, on July 14, 1994.     

Inverse programming and the linear vector maximization problem

This paper presents a new concept of efficient solution for the linear vector maximization problem. Briefly, these solutions are efficient with respect to the constraints, in addition to being efficient with respect to the multiple objectives. The duality theory of linear vector maximization is developed in terms of this solution concept and then is used to formulate the problem as a linear program.This research has been partially supported by grants from the Canada Council and the National Research Council of Canada.     

Proper inequality constraints and maximization of index vectors

For obtaining the set of all quasi-supremal index vectors (or all maximal index vectors, or all Pareto-optimal solutions) of a multiple-objective optimization problem, we present, in this paper, the method of proper inequality constraints, which does not rely on any convexity condition at all, but by which one can obtain the entire desired set. This method is based on the observation that optimizing the index of one of the objectives, with some arbitrary bounds assigned to all other objectives, may still result in inferior solutions, unless these bounds areproper. Various necessary and/or sufficient conditions are presented for the properness test.This work was supported by the National Science Foundation under Grant No. GK-32701.     

带基数约束的次模+超模(BP)函数最大化问题的流算法

本文研究在基数约束下具有单调性的次模+超模函数最大化问题的流模型。该问题在数据处理、机器学习和人工智能等方面都有广泛应用。借助于目标函数的收益递减率（$\gamma$）,我们设计了单轮读取数据的过滤-流算法,并结合次模、超模函数的全局曲率（$\kappa^{g}$）得到算法的近似比为$\min\left\{\frac{（1-\varepsilon）\gamma}{2^{\gamma}},1-\frac{\gamma}{2^{\gamma}（1-\kappa^{g}）^{2}}\right\}$。数值实验验证了过滤-流算法对BP最大化问题的有效性并且得出：次模函数和超模函数在同量级条件下,能保证在较少的时间内得到与贪婪算法相同的最优值。     

Optimal investment, consumption and retirement choice problem with disutility and subsistence consumption constraints

In this paper we consider a general optimal consumption-portfolio selection problem of an infinitely-lived agent whose consumption rate process is subject to subsistence constraints before retirement. That is, her consumption rate should be greater than or equal to some positive constant before retirement. We integrate three optimal decisions which are the optimal consumption, the optimal investment choice and the optimal stopping problem in which the agent chooses her retirement time in one model. We obtain the explicit forms of optimal policies using a martingale method and a variational inequality arising from the dual function of the optimal stopping problem. We treat the optimal retirement time as the first hitting time when her wealth exceeds a certain wealth level which will be determined by a free boundary value problem and duality approaches. We also derive closed forms of the optimal wealth processes before and after retirement. Some numerical examples are presented for the case of constant relative risk aversion (CRRA) utility class.     

带有优惠券销售的商品利润模型及其求解

根据"满100元返x元"的优惠券的特点,建立了商场商品在保持原来定价的基础上、以商家利润最大化为目的的数学模型;同时,利用遗传算法对此模型优化求解,仿真结果说明该模型及其解法具有一定的实用价值.     

Fast and accurate X‐ray fluorescence computed tomography imaging with the ordered‐subsets expectation maximization algorithm

The ordered‐subsets expectation maximization algorithm (OSEM) is introduced to X‐ray fluorescence computed tomography (XFCT) and studied; here, simulations and experimental results are presented. The simulation results indicate that OSEM is more accurate than the filtered back‐projection algorithm, and it can efficiently suppress the deterioration of image quality within a large range of angular sampling intervals. Experimental results of both an artificial phantom and cirrhotic liver show that with a satisfying image quality the angular sampling interval could be improved to save on the data‐acquisition time when OSEM is employed. In addition, with an optimum number of subsets, the image reconstruction time of OSEM could be reduced to about half of the time required for one subset. Accordingly, it can be concluded that OSEM is a potential method for fast and accurate XFCT imaging.     

跳扩散环境下考虑红利支付的动态资产配置问题研究

研究资产价格带跳环境下红利支付对投资者资产配置的影响,投资者将其财富在风险资产和无风险资产中进行分配,在终端财富预期效用最大化标准下,利用动态规划原理建立的HJB方程推导最优配置策略,并得到最优动态资产配置策略的近似解.最后通过数值模拟,分析了跳和红利支付对投资者最优配置策略的影响.结果表明在跳发生的情况下,不管跳的大小和方向如何,投资者都会减少其在风险资产中的配置头寸,同时带有红利支付的资产比不带红利支付的资产对投资者更具吸引力.     

A new approach for parameter estimation of finite Weibull mixture distributions for reliability modeling

The aim of this paper is to model lifetime data for systems that have failure modes by using the finite mixture of Weibull distributions. It involves estimating of the unknown parameters which is an important task in statistics, especially in life testing and reliability analysis. The proposed approach depends on different methods that will be used to develop the estimates such as MLE through the EM algorithm. In addition, Bayesian estimations will be investigated and some other extensions such as Graphic, Non-Linear Median Rank Regression and Monte Carlo simulation methods can be used to model the system under consideration. A numerical application will be used through the proposed approach. This paper also presents a comparison of the fitted probability density functions, reliability functions and hazard functions of the 3-parameter Weibull and Weibull mixture distributions using the proposed approach and other conventional methods which characterize the distribution of failure times for the system components. GOF is used to determine the best distribution for modeling lifetime data, the priority will be for the proposed approach which has more accurate parameter estimates.     

商品销售利润最大化模型及最优广告策略的确定

本文借助于广告方程所揭示出的商品销量与广告费用之间的动态规律；再利用分布参数系统建模研究企业供给的动态分布状态；在以广告支出作为控制变量的前提下，探讨了为使商品销售利润最大化，在产品的不同生命周期所应该采取的最优广告策略问题，并给出了某一时刻的商品需求量的预测方程。本文可为商家制定最优广告策略提供科学的参考依据。