A Primal-dual Steepest-edge Method for Even-flow Harvest Scheduling Problems

The even-flow harvest scheduling problem arises when the forestry agency has evolved into a rigid non-declining even-flow policy. In this paper, we investigate model formulation and solution strategies for the even-flow harvest scheduling problem. A multiple-objective linear programming problem is formulated for even-flow harvest scheduling problems with multiple-site classes and multiple periods. The aim of this problem is to simultaneously maximize a desired harvest-volume per hectare for each period of planning horizon and the total economic return. A block diagonal constraint structure, with many sets of network sub-problems and a set of coupling constraints, is identified in this linear programming problem. A longest path method for each of network sub-problems and a primal-dual steepest-edge algorithm for the entire problem are developed. The developed algorithm has been coded in Borland C++ and implemented on a personal computer. An illustrative example is used to display the detailed procedure for the developed algorithm and a real-world case study is used to show the trade-off between desired even-flow harvest volume policy and total economic return. Results show the potential benefits of this approach.     

应用原对偶方法光滑向量的四阶算子分裂方法

高阶算子分裂方法在改善图像边缘阶梯化、提高计算效率等问题上有很好的作用,其主要思想是将四阶的偏微分方程分裂成两个二阶的偏微分方程分别求解,先进行向量光滑,然后再进行图像重构。相对于第一步的一般显式数值迭代方法,本文应用原对偶格式进行变量替换,应用拟牛顿进行向量光滑。数值结果表明,该方法很好地提高了信噪比,且视觉效果显著。     

原对偶积极集法求解改进的有界约束图像恢复问题

为了提高模糊加噪声图像的恢复质量,提出了一种用于图像恢复处理的改进的带约束的正则化模型。该模型首先利用Levine等人提出的变指数、线性增长函数作为正则项,并根据图像局部特征选择合适的正则参数,这样既保留了总变差正则化方法在恢复图像边缘方面的优势,又减少了梯子现象;其次,为进一步提高恢复图像的质量,在此基础上再添加有界约束条件,如将灰度值固定在某范围内,以形成约束优化问题。由于它的求解相对复杂,为此可应用原对偶积极集法求解,其实质就是用半光滑Newton法来求解由约束优化问题转化所得到的方程组。数值实验表明,此方法是可行的和有效的。     

Computing the Kantorovich Distance for Images

Computing the Kantorovich distance for images is equivalent to solving a very large transportation problem. The cost-function of this transportation problem depends on which distance-function one uses to measure distances between pixels.In this paper we present an algorithm, with a computational complexity of roughly order (N2), where N is equal to the number of pixels in the two images, in case the underlying distance-function is the L1-metric, an approximation of the L2-metric or the square of the L2-metric; a standard algorithm would have a computational complexity of order (N3). The algorithm is based on the classical primal-dual algorithm.The algorithm also gives rise to a transportation plan from one image to the other and we also show how this transportation plan can be used for interpolation and possibly also for compression and discrimination.     

基于高阶马尔科夫随机场的图像去噪声研究

在图像去噪声处理中,高阶马尔科夫随机场通过最小化能量函数达到最优的去噪声结果。为了提高能量函数的优化性能,本文在马尔科夫随机场子模性的基础上对原始问题和对偶问题进行了分析,提出了一种基于原始-对偶方法的子模块之和方法。首先,描述了马尔科夫随机场的线性规划及其对偶问题,并介绍了子模块之和流方法。接下来,通过对子模块之和流方法的原始问题和对偶问题进行分析,提出了同时满足派系松弛和一元松弛条件的近似解计算方法。实验表明,本文提出的方法与四种典型的图像去噪声方法相比具有更好的效果和更短的运行时间。     

排污权交易下的多能源联供系统优化调度

随着节能减排与能源高效利用的不断推进,基于能源综合利用的多能源联供系统解决了多种能源的供应问题,是供能技术发展的方向和趋势．结合目前相继出台的排污权交易（Emission Trading）机制,提出排污权交易下的多能源联供系统优化调度方式．首先分析完全竞争和寡头竞争市场模式下的排污权交易价格,通过理论分析获得多能源联供系统的排污权交易成本的数学期望．在此基础上,以系统成本最小为目标,考虑供需平衡约束以及能源平衡约束,提出多能源联供系统的优化调度模型,并运用非线性原一对偶内点算法求解该模型．最后,以具有热电联供特征的广东理文造纸有限公司为例说明所提出的优化调度方式的有效性和可行性．     

原-对偶内点法和预测-校正内点法在最优潮流的应用

最优潮流问题在数学上是一个带约束条件的优化问题,其模型包括目标函数以及等式约束条件和不等式约束条件。利用原-对偶内点法和预测-校正内点法进行最优潮流的计算,原-对偶内点法是在保持原始可行性和对偶可行性的同时,沿一条原-对偶路径寻找最优解。预测-校正法在进行泰勒展开时保留了高阶项,首先通过修正方程计算仿射方向,在计算得到仿射扰动因子后回代入修正方程得到校正方向,进而得到修正量。预测-校正法具有比原-对偶法更好的收敛性,用Matlab实现了原-对偶内点法和预测-校正内点法进行潮流优化计算,并用算例进行了验证。     

一种求解最大输电能力的模糊算法

将模糊集理论和原始-对偶内点法应用于求解在最不利的负荷增长方式下并具有可伸缩不等式约束的最大输电能力问题。试验系统的计算表明,选用最不利的负荷增长方式,能更加准确地求得系统最大输电能力的下限值;将部分不等式约束模糊化,可求解出更加符合实际情况的最大输电能力。     

Acceleration-level repetitive motion planning of redundant planar robots solved by a simplified LVI-based primal-dual neural network

In this paper, we propose a novel repetitive motion planning (RMP) scheme at the joint-acceleration level (termed, the acceleration-level RMP scheme, the ARMP scheme), which incorporates joint-angle limits, joint-velocity limits and joint-acceleration limits. To do this, Zhang et al's neural-dynamic method is employed to derive and design such an ARMP scheme. Such a scheme is then reformulated as a quadratic program (QP). To solve this QP problem online, a simplified linear-variational-inequality based primal-dual neural network (i.e., S-LVI-PDNN) is designed. With simple piecewise-linear dynamics and global exponential convergence to the optimal solution, such an S-LVI-PDNN solver can handle the strictly convex QP problem in an inverse-free manner. Finally, three given tasks, i.e., rhombic path, straight-line path and square path tracking tasks, are fulfilled by three-link, four-link and five-link planar robot arms, respectively. Computer-simulation and physical experiment results validate the physical realizability, efficacy and accuracy of the ARMP scheme and the corresponding S-LVI-PDNN solver.     

Group Symmetry in Interior-Point Methods for Semidefinite Program

A class of group symmetric Semi-Definite Program (SDP) is introduced by using the framework of group representation theory. It is proved that the central path and several search directions of primal-dual interior-point methods are group symmetric. Preservation of group symmetry along the search direction theoretically guarantees that the numerically obtained optimal solution is group symmetric. As an illustrative example, we show that the optimization problem of a symmetric truss under frequency constraints can be formulated as a group symmetric SDP. Numerical experiments using an interior-point algorithm demonstrate convergence to strictly group symmetric solutions.