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1.
A tutorial on geometric programming   总被引:3,自引:0,他引:3  
A geometric program (GP) is a type of mathematical optimization problem characterized by objective and constraint functions that have a special form. Recently developed solution methods can solve even large-scale GPs extremely efficiently and reliably; at the same time a number of practical problems, particularly in circuit design, have been found to be equivalent to (or well approximated by) GPs. Putting these two together, we get effective solutions for the practical problems. The basic approach in GP modeling is to attempt to express a practical problem, such as an engineering analysis or design problem, in GP format. In the best case, this formulation is exact; when this is not possible, we settle for an approximate formulation. This tutorial paper collects together in one place the basic background material needed to do GP modeling. We start with the basic definitions and facts, and some methods used to transform problems into GP format. We show how to recognize functions and problems compatible with GP, and how to approximate functions or data in a form compatible with GP (when this is possible). We give some simple and representative examples, and also describe some common extensions of GP, along with methods for solving (or approximately solving) them.  相似文献
2.
Convex piecewise-linear fitting   总被引:1,自引:1,他引:0  
We consider the problem of fitting a convex piecewise-linear function, with some specified form, to given multi-dimensional data. Except for a few special cases, this problem is hard to solve exactly, so we focus on heuristic methods that find locally optimal fits. The method we describe, which is a variation on the K-means algorithm for clustering, seems to work well in practice, at least on data that can be fit well by a convex function. We focus on the simplest function form, a maximum of a fixed number of affine functions, and then show how the methods extend to a more general form.  相似文献
3.
Based on queuing theory, a nonlinear optimization model is proposed in this paper, which has the service load as its objective function and includes three inequality constraints of Work In Progress (WIP). A novel transformation of optimization variables is also devised and the constraints are properly combined so as to make this model into a convex one from which the Lagrangian function and the Karurh Kuhn Tucker (KKT) conditions are derived. The interior-point method for convex optimization is presented here as a computationaUy efficient tool. Finally, this model is evaluated on a real example, from which such conclusions are reached that the optimum result can ensure the full utilization of machines and the least amount of WIP in manufacturing systems; the interior-point method needs fewer iterations with significant computational savings and it is possible to make nonlinear and complicated optimization problems convexified so as to obtain the optimum.  相似文献
4.
In this paper we develop a new theory of static equilibrium in congested transportation networks. We show that under some natural assumptions, the Wardrop principle leads to a very strong relation between the loading of the arc, arc flow and arc travel time. This relation allows us to simplify significantly the arc performance model. We show that instead of fixing a functional form of travel time function, we can obtain equilibrium solutions for static traffic assignment models using only some natural bounds for arc travel time and arc flow. We compare the results of our model with the results of standard Beckmann model.  相似文献
5.
研究了快速求解具有时间约束的机械臂轨迹规划问题,提出了一种基于凸规划的轨迹规划方法。该方法针对机械臂轨迹规划中动力学约束非线性强、时间约束不易处理的问题,首先通过变量替换,将非线性约束转化为线性约束,然后添加新的约束,将原始非凸优化问题转化为凸规划问题,在此基础上,将其写作二阶锥规划(SOCP)形式,使用SeDuMi等优化工具包近似实时求解。该方法具有以下优点:计算高效,凸规划问题能够在多项式时间内得到求解;算法全局稳定,能收敛到全局最优解,不需要提供优化初值;可扩展性强,工业机器人的多种约束以及性能指标如加速度平滑约束、功率等均可扩充。仿真实验表明,与现有方法相比,该方法能够有效提高轨迹规划的效率,机器人的轨迹规划可以近似实时求解。  相似文献
6.
将发射阵的期望主瓣幅度响应波束设计转化为凸优化问题,并利用cvx工具箱求解最优加权。首先,根据期望波束的主瓣范围,将空间区域分为主瓣区域和旁瓣区域,再在主瓣区域内将设计波束和期望波束之差的2-范数最小化,并将设计波束图旁瓣级控制在期望值之下。最后,利用cvx工具箱对该凸优化问题进行求解,获得满足要求的设计波束图。通过计算机仿真对所提波束图设计方法的有效性进行了验证。  相似文献
7.
First, we summarize our convex optimization method to solve the static approach of limit analysis. Then, we present the main features of a quadratic extension of a recently proposed mixed finite element method of the kinematic approach. Both methods are applied to obtain precise solutions to a forming problem with Gurson and Drucker-Prager materials. Finally, in order to analyze the criterion of “Porous Drucker-Prager” materials, the Gurson micro-macro model involving a Drucker-Prager matrix containing cylindrical cavities is investigated. Comparing previous results shows, among other things, a similarity in the compression case not always observed for the “Porous von Mises” material between cylindrical and spherical cases.  相似文献
8.
Two adaptive discretization frameworks are tested for computerized tomography (CT) data reconstruction. Removal of inactive pixels is primary motivation. Efficient and user independent entropy optimized masking is employed for spatial filtering purposes. Density of nodes at high gradient of reconstructed physical property is used as adaptation criterion. An alternative option, independent from noisy projection data and nature of the physical properties, is also discussed. Sensitivity analysis between the uniform and nonuniform (evolved via adaptive route) reconstruction grid reveals the utility of nonuniform grids. Iterative and transform based reconstruction techniques are used. Outcomes are tested successfully on three real world projection data from two different compact CT setups and one commercial high-resolution micro-CT scanner.  相似文献
9.
In various manufacturing applications such as steel, composites, and textile production, anomaly detection in noisy images is of special importance. Although there are several methods for image denoising and anomaly detection, most of these perform denoising and detection sequentially, which affects detection accuracy and efficiency. Additionally, the low computational speed of some of these methods is a limitation for real-time inspection. In this article, we develop a novel methodology for anomaly detection in noisy images with smooth backgrounds. The proposed method, named smooth-sparse decomposition, exploits regularized high-dimensional regression to decompose an image and separate anomalous regions by solving a large-scale optimization problem. To enable the proposed method for real-time implementation, a fast algorithm for solving the optimization model is proposed. Using simulations and a case study, we evaluate the performance of the proposed method and compare it with existing methods. Numerical results demonstrate the superiority of the proposed method in terms of the detection accuracy as well as computation time. This article has supplementary materials that includes all the technical details, proofs, MATLAB codes, and simulated images used in the article.  相似文献
10.
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