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Predictor-corrector interior-point algorithm for linearly constrained convex programming

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Journal of Central South University 2001年第3期13卷 208-212页

作者： LIANG Xi-ming (College of Information Science & Engineering, Central South University, Changsh a 410083, China) College of Information Science & Engineering Central South University Changsha China

Active set method and gradient projection method are curre nt ly the main approaches for linearly constrained convex programming. Interior-po int method is one of the most effective choices for linear programming. In the p aper a predictor-corrector interior-point algorithm for linearly constrained c onvex programming under the predictor-corrector motivation was proposed. In eac h iteration, the algorithm first performs a predictor-step to reduce the dualit y gap and then a corrector-step to keep the points close to the central traject ory. Computations in the algorithm only require that the initial iterate be nonn egative while feasibility or strict feasibility is not required. It is proved th at the algorithm is equivalent to a level-1 perturbed composite Newton method. Numerical experiments on twenty-six standard test problems are made. The result s show that the proposed algorithm is stable and robust.

关键词： linearly constrained convex programming predictor-correct or interior-point algorithm numerical experiment

RADIAL convex SOLUTIONS OF A SINGULAR DIRICHLET PROBLEM WITH THE MEAN CURVATURE OPERATOR IN MINKOWSKI SPACE

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Acta Mathematica Scientia 2019年第2期39卷 395-402页

作者：梁载涛杨艳娟 School of Mathematics and Big Data Anhui University of Science and Technology College of Sciences Hohai University

In this paper, we study the existence of nontrivial radial convex solutions of a singular Dirichlet problem involving the mean curvature operator in Minkowski space. The proof is based on a well-known fixed point theo... 详细信息

关键词： radial convex solutions singular Dirichlet problem mean curvature operator fixed point theorem in cones

Uniform design over a convex polyhedron

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Chinese Science Bulletin 1999年第2期44卷 112-114页

作者： FANG Kaitai , TIAN Guoliang XIE Minyu Hong Kong Baptist University, Kowloon, Hong Kong, China Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing 100080, China Central China Normal University, Wuhan 430070, ChinaCorresponding author: Present address: Department of Probability and Statistics, Peking University, Beijing 100871, China Hong Kong Baptist University Hong Kong China Institute of Applied Mathematics Chinese Academy of Sciences Beijing China Central China Normal University Wuhan China

A new method, called the simplex method, is proposed to generate the uniform design over a convex polyhedron in n-dimensional Euclidean

关键词： convex polyhedron experimental design uniform design.

An Introduction to convex Optimization Theory in Communication Signals Recognition

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Journal of Harbin Institute of Technology(New Series) 2013年第5期20卷 14-19页

作者： Jin-Feng Pang Yun Lin Xiao-Chun Xu Zheng Dou Zi-Cheng Wang College of Information and Communication Engineering Harbin Engineering University

In this paper,convex optimization theory is introduced into the recognition of communication signals. The detailed content contains three parts. The first part gives a survey of basic concepts,main technology and recognition model of convex optimization theory. Special emphasis is placed on how to set up the new recognition model of communication signals with multisensor reports. The second part gives the solution method of the recognition model,which is called Logarithmic Penalty Barrier Function. The last part gives several numeric simulations,in contrast to D-S evidence inference method,this new method can also generate reasonable recognition results. Moreover,this new method can deal with the form of sensor reports which is more general than that allowed by the D-S evidence inference method,and it has much lower computation complexity than that of D-S evidence inference method. In addition,this new method has better recognition result,stronger anti-interference and robustness. Therefore,the convex optimization methods can be widely used in the recognition of communication signals.

关键词： convex optimization theory signal recognition D-S evidence theory logarithmic penalty barrier function

Removing mixed noise in low rank textures by convex optimization

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Computational Visual Media 2016年第3期2卷 267-276页

作者： Xiao Liang Institute for Advanced Study Tsinghua University

This paper introduces a new low rank texture image denoising algorithm, which can restore low rank texture contaminated by both Gaussian and salt-and-pepper noise. The algorithm formulates texture image denoising in terms of solving a low rank matrix optimization problem. Simply assuming low rank is insufficient to describe the properties of natural images, causing high noise amplitudes which lead to unsatisfactory denoising results or serious loss of image details. Thus, in addition to the low rank assumption,the continuity of natural images is also assumed by the algorithm, by adding a total variation regularizer to the optimization objective function. We further give an effective algorithm to solve this optimization problem. By combining the low rank and continuity assumptions, the proposed algorithm overcomes the deficiencies of using either the low rank assumption or total variation regularization alone. Experiments show that our algorithm can effectively remove mixed noise in low rank texture images, and is better than existing algorithms in both its subjective visual effects and in terms of quantitative objective measures.

关键词： image denoising low rank texture total variation convex optimization augmented Lagrangian method

An isoperimetric deficit upper bound of the convex domain in a surface of constant curvature

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Science China Mathematics 2010年第8期53卷 1941-1946页

作者： LI Ming & ZHOU JiaZu School of Mathematics and Statistics,Southwest University,Chongqing 400715,China School of Mathematics and Statistics Southwest University Chongqing China

In this paper,we give a reverse analog of the Bonnesen-style inequality of a convex domain in the surface X of constant curvature,that is,an isoperimetric deficit upper bound of the convex domain in X.The result is an... 详细信息

关键词： Kinematic formula the surface of constant curvature isoperimetric deficit convex set

THE MINIMAX DIRECTION FOR THE DIRECT PRODUCT OF A convex CONE WITH ITS APPLICATION TO TESTING PROBLEMS

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Chinese Annals of Mathematics,Series B 1992年第1期13卷 80-85页

作者：史宁中 Department of Mathematics Northeast Normal UniversityChangchunJilinChina.

Let C be a closed convex cone in R^k and let C^p be the p-th direct product of C.Thispaper gives some results of the minimax direction with respect to C^p and an innerproduct based on(?),where is a k×k diagonal matrix with positive diagonalelements,is a p×p positive definite matrix and is the Kronecker product ofand.It is also shown that the results may be applied to test the homogeneity of knormal mean vectors where the mean vectors are restricted by a given partial order.

关键词： Kronecker diagonal restricted convex CONE definite homogeneity uniformly sided generalize

Approximation Algorithms for Solving Packing Problems of convex Polygons in Plane

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Science China Mathematics 1993年第1期36卷 100-108页

作者：李庆华鄢勇刘健 Department of Computer Science & Engineering Huazhong University of Science & Technology

The problem of initial collision between convex polygons is studied in detail, and a fast algorithm for finding the embedded depth is obtained, by which the fast approximate algorithm for solving packing problems of c... 详细信息

关键词： convex polygon embedded depth squeezing elastic potential initial collision minimum collision distance.

Computer Aided Design Technology for convex Faceted Gem Cuts Based on the Half-Edge Data Structure

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Journal of Beijing Institute of Technology 2019年第3期28卷 585-597页

作者： Linhong Xu Xiangnan Li Jianhua Rao Yuan Han Zhipeng Li Jichun Li School of Mechanical Engineering and Electronic Information China University of Geosciences (Wuhan)

Aiming to increase the efficiency of gem design and manufacturing, a new method in computer-aided-design (CAD) of convex faceted gem cuts (CFGC) based on Half-edge data structure (HDS), including the algorithms for the implementation is presented in this work. By using object-oriented methods, geometrical elements of CFGC are classified and responding geometrical feature classes are established. Each class is implemented and embedded based on the gem process. Matrix arithmetic and analytical geometry are used to derive the affine transformation and the cutting algorithm. Based on the demand for a diversity of gem cuts, CAD functions both for free-style faceted cuts and parametric designs of typical cuts and visualization and human-computer interactions of the CAD system including two-dimensional and three-dimensional interactions have been realized which enhances the flexibility and universality of the CAD system. Furthermore, data in this CAD system can also be used directly by the gem CAM module, which will promote the gem CAD/CAM integration.

关键词： Half-edge data structure convex faceted gem cuts (CFGC) computer aided design (CAD)