Computing Optimal Beams in Two and Three Dimensions

The problem of computing an optimal beam among weighted regions (called the optimal beam problem) arises in several applied areas such as radiation therapy, stereotactic brain surgery, medical surgery, geological exploration, manufacturing, and environmental engineering. In this paper, we present computational geometry techniques that enable us to develop efficient algorithms for solving various optimal beam problems among weighted regions in two and three dimensional spaces. In particular, we consider two types of problems: the covering problems (seeking an optimal beam to contain a specified target region), and the piercing problems (seeking an optimal beam of a fixed shape to pierce the target region). We investigate several versions of these problems, with a variety of beam shapes and target region shapes in 2-D and 3-D. Our algorithms are based on interesting combinations of computational geometry techniques and optimization methods, and transform the optimal beam problems to solving a collection of instances of certain special non-linear optimization problems. Our approach makes use of interesting geometric observations, such as utilizing some new features of Minkowski sums.     

Computer-aided formulation and optimal control of an integrated production system for competitive products

An integrated production, inventory and advertising system has been formulated based on control engineering principles. In this system, the customer's demand is satisfied from stock, which in turn is replenished from production facilities. But sales reflect the advertising effort, present as well as past. The past effort has been considered as a delay with an assumed delay period. The problem is formulated as a state and observation model. Out of this an augmented model of state and parameters is formed. The parameters describing the model are estimated from MAP discrete filter algorithm. It is shown that sales of product 1 or product 2 at (k + l)th period is effected by sales and advertising of product 1 or product 2 at the kth period, and also by sales and advertising of product 2 or product 1 at (k-θ)th period, where 6 is the delay.     

非流动性市场中的跨期最优消费和投资策略

本文在Merton跨期最优消费和资产组合的理论框架内引入非流动性资产,构造了一个三资产的连续时间经济模型,探讨流动性约束对投资者最优消费和投资决策的影响。本文用动态规划方法给出了跨期优化问题的解析解。数值分析表明对投资者而言,非流动性资产的真实价值低于其市值,必须引入影子价格来刻划这种流动性效应;流动性约束降低了投资者的福利,并且显著地影响到投资者的消费和投资策略。     

西部地区电能与环境协调发展系统中政府规制偏好研究

电力产业作为重要的能源部门之一,对整个国民经济发展起到巨大的基础性支撑作用,但其中的火力发电行业所造成的环境污染也给社会带来一系列问题,我国西部地区也不例外。通过将污染物减排过程对经济产生的正的外部性考虑进电能与环境发展系统,并对政府进行理性人的假设,设计电能与环境协调发展系统中的政府规制效用函数,运用计量经济学方法和微观经济学中理性人效用最大化的条件,对我国西部地区1995~2005年电能与环境协调发展系统中的政府规制偏好进行了定量分析。发现在环境法规逐渐完善的基础上,政府对于电能生产的偏好有所下降,对污染物减排的偏好逐渐上升。