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A LQP BASED INTERIOR PREDICTION-CORRECTION METHOD FOR NONLINEAR COMPLEMENTARITY PROBLEMS

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Journal of Computational Mathematics 2006年第1期24卷 33-44页

作者： bing-sheng he Li-zhi Liao Xiao-ming Yuan Department of Mathematics Nanjing University Nanjing 210093 China Department of Mathematics Hong Kong Baptist University Hong Kong China Department of Mathematics City University of Hong Kong Hong Kong China

To solve nonlinear complementarity problems （NCP）, at each iteration, the classical proximal point algorithm solves a well-conditioned sub-NCP while the Logarithmic-Quadratic Proximal （LQP） method solves a system of nonlinear equations （LQP system）. This paper presents a practical LQP method-based prediction-correction method for NCP. The predictor is obtained via solving the LQP system approximately under significantly relaxed restriction, and the new iterate （the corrector） is computed directly by an explicit formula derived from the original LQP method. The implementations are very easy to be carried out. Global convergence of the method is proved under the same mild assumptions as the original LQP method. Finally, numerical results for traffic equilibrium problems are provided to verify that the method is effective for some practical problems.

关键词： Logarithmic-Quadratic proximal method Nonlinear complementarity problems Prediction-correction Inexact criterion

ALTERNATING PROJECTION BASED PREDICTION-CORRECTION METHODS FOR STRUCTURED VARIATIONAL INEQUALITIES

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Journal of Computational Mathematics 2006年第6期24卷 693-710页

作者： bing-sheng he Li-zhi Liao Mai-jian Qian Department of Mathematics Nanjing University Nanjing 210093 China Department of Mathematics Hong Kong Baptist University Hong Kong China Department of Mathematics California State University FuUerton CA 92834 USA

The monotone variational inequalities VI（Ω, F） have vast applications, including optimal controls and convex programming. In this paper we focus on the VI problems that have a particular splitting structure and in which the mapping F does not have an explicit form, therefore only its function values can be employed in the numerical methods for solving such problems. We study a set of numerical methods that are easily implementable. Each iteration of the proposed methods consists of two procedures. The first （prediction） procedure utilizes alternating projections to produce a predictor. The second （correction） procedure generates the new iterate via some minor computations. Convergence of the proposed methods is proved under mild conditions. Preliminary numerical experiments for some traffic equilibrium problems illustrate the effectiveness of the proposed methods.

关键词： Structured variational inequality Monotonicity Prediction-correction method.

Alternating Direction Method of Multipliers for Linear Programming

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Journal of the Operations Research Society of China 2016年第4期4卷 425-436页

作者： bing-sheng he Xiao-Ming Yuan Department of Mathematics South University of Science and Technology of ChinaShenzhen 518055China Department of Mathematics Nanjing UniversityNanjing 210023China Department of Mathematics Hong Kong Baptist UniversityHong KongChina

Linear programming is the core problem of various operational research *** dominant approaches for linear programming are simplex and interior point *** this paper,we showthat the alternating direction method of multipliers(ADMM),which was proposed long time ago while recently found more and more applications in a broad spectrum of areas,can also be easily used to solve the canonical linear programming *** resulting per-iteration complexity is O(mn)where m is the constraint number and n the variable *** each iteration,there are m subproblems that are eligible for parallel computation;each requiring only O(n)*** is no inner iteration as *** thus introduce the newADMMapproach to linear programming,which may inspire deeper research for more complicated scenarios with more sophisticated results.

关键词： Continuous optimization Linear programming Alternating direction method of multipliers

SOLVING TRUST REGION PROBLEM IN LARGE SCALEOPTIMIZATION

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Journal of Computational Mathematics 2000年第1期18卷 1-12页

作者： bing-sheng he(Department of Mathematics, Nanjing University, Naming 210093, China) 南京大学江苏南京 210093

Presents a study which introduced a method for solving trust region problem in scale minimization. Review of the conjugate gradient method (CG) and the projection and contraction (PC) method; Convergence behavior of t... 详细信息

关键词： trust region problem conjugate gradient method projection and contraction method

A GOLDSTEIN'S TYPE PROJECTION METHOD FOR A CLASSOF VARIANT VARIATIONAL INEQUALITIES

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Journal of Computational Mathematics 1999年第4期17卷 425-434页

作者： bing-sheng he(Department of Mathematics, Nanjing University, Nanjing 210008, China) Department of Mathematics Nanjing University Nanjing 210008 China

Some optimization problems in mathematical programming can be translated to a variant variational inequality of the following form: Find a vectoru*, such that This paper presents a simple iterative method for solving this class of variational inequalities. The method can be viewed as an extension of theGoldstein's projection method. Some results of preliminary numerical experiments are given to indicate its applications.

关键词： Variational inequality Goldstein projection method.

Block-Wise ADMM with a Relaxation Factor for Multiple-Block Convex Programming

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Journal of the Operations Research Society of China 2018年第4期6卷 485-505页

作者： bing-sheng he Ming-Hua Xu Xiao-Ming Yuan Department of Mathematics South University of Science and TechnologyShenzhen 518055GuangdongChina Department of Mathematics Nanjing UniversityNanjing 210093China School of Mathematics and Physics Changzhou UniversityChangzhou 213164JiangsuChina Department of Mathematics The University of Hong KongHong KongChina

It has been shown that the alternating direction method of multipliers(ADMM)is not necessarily convergent when it is directly extended to a multiple-block linearly constrained convex minimization model with an objective function that is in the sum of more than two functions without coupled ***,we pro-posed the block-wise ADMM,which was obtained by regrouping the variables and functions of such a model as two blocks and then applying the original ADMM in *** note is a further study on this topic with the purpose of showing that a well-known relaxation factor proposed by Fortin and Glowinski for iteratively updat-ing the Lagrangian multiplier of the originalADMMcan also be used in the block-wise *** thus propose the block-wise ADMM with Fortin and Glowinski’s relax-ation factor for the multiple-block convex minimization *** the block-wise ADMM,we also suggest further decomposing the resulting subproblems and regular-izing them by proximal terms to ensure the *** the block-wise ADMM with Fortin and Glowinski's relaxation factor,its convergence and worst-case conver-gence rate measured by the iteration complexity in the ergodic sense are derived.

关键词： Convex programming Operator splitting methods Alternating direction method of multipliers Fortin and Glowinski’s relaxation factor

Multifactorial analysis of recurrence of cholecystolithiasis in Shanghai area

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World Journal of Gastroenterology 1999年第1期5卷 36-38页

作者： CheN Pei, WANG bing sheng and he Lian Qi

AIM To explore the risk factors of gallbladder stone recurrence. METHODS A multifactorial analysis was made for 1058 patients in Shanghai area whose gallbladder stones disappeared after different kinds of nonsurgical therapy, including oral litholytic therapy, extracorporeal shock wave lithotripsy and percutaneous choledocholithotripsy. Serum level of insulin and total bile acid were determined in 122 patients. RESULTS After 1 8 8 years of follow up, the recurrence rate of gallbladder stone was 11 6%, 22 4%, 29 5%, 36 4%, 39 3% and 39 7% respectively within 1, 2, 3, 4, 5 and over 5 years. The risk factors for the recurrence are: primary multiple gallstones ( P he recurrence of cholecystolithiasis is related to overintake of high fat and high cholesterol food, and might also be related to low level of serum insulin.

关键词： cholecystolithiasis/therapy recurrence follow up studies

Effects of Iron on Growth and Intracellular Chemical Contents of Microcystis aeruginosa

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Biomedical and Environmental Sciences 2010年第1期23卷 48-52页

作者： CHONG WANG,HAI-NAN KONG ,XIN-ZE WANG,HAO-DONG WU,YAN LIN,AND sheng-bing he School of Environmental Science and Engineering,Shanghai Jiao Tong University,Shanghai 200240,China [a] School of Environmental Science Engineering Shanghai Jiao Tong University Shanghai 200240 China

Objective To investigate the effect of iron on the growth, physiology and photosynthesis of cyanobacteria. Methods A gradient of iron concentrations was employed to investigate the growth, photo-pigments （chlorophyll A and phycocyanin）, and cell chemical contents （C, N, P） of Microcystis aeruginosa in response to different iron additions. Results The specific growth rate during the exponential growth phase, as well as the cell chlorophyll A and the phycocyanin content, was limited by iron below 12.3μmol Fe.L^-1. The growth was inhibited when the iron concentration was at 24.6 μmol Fe.L^-1. The cell chlorophyll A and the phycocyanin content were saturated when the iron concentration was above 12.3μmol Fe.L^-1 and declined slightly at 24.6 μmol Fe.L^-1. At a low iron concentration （about 6.15 μmol Fe-L^-1 and less）, the cell nitrogen and carbohydrate content were iron limited, and the variation of the cell phosphorus content was similar to that of the nitrogen and carbohydrate, with a transition point of 12.3 μmol Fe.L^-1. Conclusion The variation ofcynobacteria growth is synchronous with that of the photo-pigments or the cell chemical content, and there exist relationships among photosynthesis, growth and internal chemical content, which could be useful for the growth estimation from the cell characteristics.

关键词： Iron Growth Photo-pigments Carbohydrate Phosphorus Nitrogen

Improvements of General Extra-gradient Method for Nonlinear Monotone Variational Inequalities

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Improvements of General Extra-gradient Method for Nonlinear ...