多项式分裂可行问题

本文研究多项式分裂可行问题,即由多项式不等式定义的分裂可行问题,包括凸与非凸、可行与不可行的问题;给出多项式分裂可行问题解集的半定松弛表示;研究其半定松弛化问题的性质;并基于这些性质建立求解多项式分裂可行问题的半定松弛算法.本文在较为一般的条件下证明了,如果分裂可行问题有解,则可通过本文建立的算法求得一个解点;如果问题...     

高校开设野外生存生活训练课程的可行性

对高校开设野外生存生活训练课程的效果及存在的问题进行了分析，论证了此课程在高校开设的可行性。     

Complexity analysis of the analytic center cutting plane method that uses multiple cuts

We analyze the complexity of the analytic center cutting plane or column generation algorithm for solving general convex problems defined by a separation oracle. The oracle is called at the analytic center of a polytope, which contains a solution set and is given by the intersection of the linear inequalities previously generated from the oracle. If the center is not in the solution set, separating hyperplanes will be placed through the center to shrink the containing polytope. While the complexity result has been recently established for the algorithm when one cutting plane is placed in each iteration, the result remains open when multiple cuts are added. Moreover, adding multiple cuts actually is a key to practical effectiveness in solving many problems and it presents theoretical difficulties in analyzing cutting plane methods. In this paper, we show that the analytic center cutting plane algorithm, with multiple cuts added in each iteration, still is a fully polynomial approximation algorithm. The research of the author is supported by NSF grant DDM-9207347, an Iowa Business School Summer Grant, and a University of Iowa Obermann Fellowship.     

Properties of the sequential gradient-restoration algorithm (SGRA), part 1: Introduction and comparison with related methods

The sequential gradient-restoration algorithm (SGRA) was developed in the late 1960s for the solution of equality-constrained nonlinear programs and has been successfully implemented by Miele and coworkers on many large-scale problems. The algorithm consists of two major sequentially applied phases. The first is a gradient-type minimization in a subspace tangent to the constraint surface, and the second is a feasibility restoration procedure. In Part 1, the original SGRA algorithm is described and is compared with two other related methods: the gradient projection and the generalized reduced gradient methods. Next, the special case of linear equalities is analyzed. It is shown that, in this case, only the gradient-type minimization phase is needed, and the SGRA becomes identical to the steepest-descent method. Convergence proofs for the nonlinearly constrained case are given in Part 2.Partial support for this work was provided by the Fund for the Promotion of Research at Technion, Israel Institute of Technology, Haifa, Israel.     

Convergence criteria for generalized gradient methods of solving locally Lipschitz feasibility problems

We prove the convergence of a class of iterative algorithms for solving locally Lipschitz feasibility problems, that is, finite systems of inequalities f _i (x)0, (i I), where each f _i is a locally Lipschitz functional on ⁿ . We also obtain a new convergence criterion for the so-called block-iterative projection methods of finding common points of finite families of convex closed subsets of ⁿ as defined by Aharoni and Censor ([3]).The work of Dan Butnariu was done while visiting the Department of Mathematics of the University of Texas at Arlington.     

A simplified homogeneous and self-dual linear programming algorithm and its implementation

We present a simplification and generalization of the recent homogeneous and self-dual linear programming (LP) algorithm. The algorithm does not use any Big-M initial point and achieves -iteration complexity, wheren andL are the number of variables and the length of data of the LP problem. It also detects LP infeasibility based on a provable criterion. Its preliminary implementation with a simple predictor and corrector technique results in an efficient computer code in practice. In contrast to other interior-point methods, our code solves NETLIB problems, feasible or infeasible, starting simply fromx=e (primal variables),y=0 (dual variables),z=e (dual slack variables), wheree is the vector of all ones. We describe our computational experience in solving these problems, and compare our results with OB1.60, a state-of-the-art implementation of interior-point algorithms.Research supported in part by NSF Grant DDM-9207347 and by an Iowa College of Business Administration Summer Grant.Part of this work was done while the author was on a sabbatical leave from the University of Iowa and visiting the Cornell Theory Center, Cornell University, Ithaca, NY 14853, USA, supported in part by the Cornell Center for Applied Mathematics and by the Advanced Computing Research Institute, a unit of the Cornell Theory Center, which receives major funding from the National Science Foundation and IBM Corporation, with additional support from New York State and members of its Corporate Research Institute.     

The primal-dual algorithm as a constraint-set-manipulation device

A general primal—dual algorithm for linearly constrained optimization problems is formulated in which the dual variables are updated by a dual algorithmic operator. Convergence is proved under the assumption that the dual algorithmic operator implies asymptotic feasibility of the primal iterates with respect to the linear constraints. A general result relating the minimal values of an infinite sequence of constrained problems to the minimal value of a limiting problem (constrained by the limit of the sequence of constraints sets) is established and invoked. The applicability of the general theory is demonstrated by analyzing a specific dual algorithmic operator. This leads to the MART algorithm for constrained entropy maximization used in image reconstruction from projections.     

企业人力资本引进投资可行性的多层次灰色评价

企业人力资本引进投资是一种高风险性的投资.为了避免投资失误并获得预期的投资效益,企业在引进人力资本之前必须开展投资可行性评价.本文以可行性研究理论为指导,从人力资本质量可行性、企业内部环境可行性和投资效益可行性三个方面建立了企业人力资本引进投资的可行性评价指标体系,并提出了运用多层次灰色评价方法进行企业人力资本引进投资可行性评价的步骤,最后用实例说明了其应用.     

A novel methodology for photometric compensation of projection display on patterned screen

We propose a novel methodology based on the projector-camera (ProCam) system to address the photometric compensation issue for the projection display on the patterned screen.The patterned screen is treated as the combination of a perfect white screen and a color modulator.The perfect white screen is used to automatically and accurately characterize the ProCam system offline using the polynomial model,and the parameters of the color modulator can be efficiently recovered by employing only two gray images based on the linear reflectance model.The experimental results show that the color artifacts of the display image can be greatly improved with this methodology,which demonstrates its feasibility and validity in the photometric compensation.     

大尺寸单晶金刚石制备的研究进展

单晶金刚石在电学,光学方面有着良好的应用前景,已经成为金刚石领域的研究焦点之一.本文论述了大尺寸单晶金刚石的制备方法、生长条件、研究现状以及存在的缺陷,概述了制备单晶金刚石过程中出现的问题并针对部分问题提出改善措施.