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Continuity of the optimal value function and optimal solutions of parametric mixed-integer quadratic programs

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Applied Mathematics(A Journal of Chinese Universities) 2010年第4期25卷 391-399页

作者： CHEN Zhi-ping HAN You-pan Department of Scientific Computing and Applied Software, Faculty of Science, Xi’an Jiaotong University, Xi’an 710049, China Department of Scientific Computing and Applied Software Faculty of Science Xi’an Jiaotong University Xi’an China

To properly describe and solve complex decision problems, research on theoretical properties and solution of mixed-integer quadratic programs is becoming very important. We establish in this paper different Lipschitz-type continuity results about the optimal value function and optimal solutions of mixed-integer parametric quadratic programs with parameters in the linear part of the objective function and in the right-hand sides of the linear constraints. The obtained results extend some existing results for continuous quadratic programs, and, more importantly, lay the foundation for further theoretical study and corresponding algorithm analysis on mixed-integer quadratic programs.

关键词： Mixed-integer quadratic program optimal value function optimal solution.

ON SOME FEASIBILITY CONDITIONS IN MPEC

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Acta Mathematica Scientia 2008年第2期28卷 289-294页

作者：周叔子白敏茹 College of Mathematics and Econometrics Hunan University

This article discusses feasibility conditions in mathematical programs with equilibrium constraints （MPECs）. The authors prove that two sufficient conditions guarantee the feasibility of these MPECs. The authors show that the two feasibility conditions are different from the feasibility condition in [2, 3], and show that the sufficient condition in [3] is stronger than that in [2].

关键词： Mathematical programs with equilibrium constraints constraints feasibility,complementarity problem quadratic program

Convergence of a Class of Stationary Iterative Methods for Saddle Point Problems

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Journal of the Operations Research Society of China 2019年第2期7卷 195-204页

作者： Yin Zhang Institute for Data and Decision Analytics The Chinese University of Hong KongShenzhen 518172China Department of Computational and Applied Mathematics Rice UniversityHouston 77005United States of America

A unified convergence theory is derived for a class of stationary iterative methods for solving linear equality constrained quadratic programs or saddle point *** class is constructed from essentially all possible splittings of the submatrix residing in the(1,1)-block of the augmented saddle point matrix that would produce non-expansive *** classic augmented Lagrangian method and alternating direction method of multipliers are two special members of this class.

关键词： Saddle point problem quadratic program Matrix splitting Stationary iterations Spectral radius Q-linear convergence

Estimation and Testing for the Parameters of AR(p)-ARCH(q) under Ordered Restriction

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Northeastern Mathematical Journal 2005年第4期21卷 475-491页

作者：王德辉宋立新史宁中 Institute of Mathematics Jilin UniversityChangchun130012 Department of Mathematics Northeast Normal UniversityChangchun130021

In this paper, we study a stationary AR（p）-ARCH（q） model with parameter vectors α and β. We propose a method for computing the maximum likelihood estimator （MLE） of parameters under the nonnegative restriction. A similar method is also proposed for the case that the parameters are restricted by a simple order： α1≥α2≥…≥αq and β1≥β2≥…≥βp. The strong consistency of the above two estimators is discussed. Furthermore, we consider the problem of testing homogeneity of parameters against the simple order restriction. We give the likelihood ratio （LR） test statistic for the testing problem and derive its asymptotic null distribution.

关键词： AR(p)-ARCH(q) model ordered restriction maximum likelihood estimator asymptotic properties quadratic program

Safe bumpless transfer control for switched systems and its applications

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Safe bumpless transfer control for switched systems and its ...

Unification and Comparison on Bi-Criteria Velocity,Acceleration and Torque Minimization Illustrated via Three-Link Planar Robot Arm

第43届中国控制会议

作者： Qian Liu Hening Yang Pan Yu Beijing Institute of Artificial Intelligence Faculty of Information Technology Beijing University of Technology

This paper considers a bumpless transfer control design problem to guarantee the asymptotic stability with safety performance for switched systems. Firstly, for a switched system, the safety condition which is expressed as a common control barrier function(CCBF) is unified with the asymptotic stability condition which is expressed as a set of safety-based multiple control Lyapunov functions(SMCLFs) in the context of real-time optimization based controllers. Then, based on an average dwell time approach,the bumpless transfer controller is designed through constructing a CCBF and SMCLFs in the context of a quadratic program(QP). Finally, the mediation of the safety performance and the asymptotic stability performance through a QP is demonstrated on two examples.

关键词： bumpless transfer safety performance average dwell time quadratic program

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Unification and Comparison on Bi-Criteria Velocity,Accelerat...

Estimation and Testing for the Parameters of AR(p)-ARCH(q) under Ordered Restriction

2011 Chinese Control and Decision Conference（CCDC）

作者： Yunong Zhang,Dongsheng Guo,Jun Li,and Kene Li The authors are with School of Information Science and Technology,Sun Yat-sen University,Guangzhou 510006,China

In this paper,the latest result that the bi-criteria redundancy-resolution schemes at different levels （i.e.,the joint-velocity,-acceleration and-torque levels） can be unified into a quadratic-programming （QP） problem formulation,is presented and summarized for redundant robot arms with joint physical *** addition,comparison on the three schemes is presented for further *** presented QP-based formulation,subject to equality,inequality and bound constraints simultaneously,is then solved online via a primaldual neural network based on linear variation inequalities （LVI）.Computer-simulation results based on PUMA560,PA10 and multi-link planar robot arms （specially,a three-link planar robot arm in this paper） have demonstrated the efficacy of the bi-criteria neural-weighting schemes,as well as the resultant QP-based unification of robots’ redundancy resolution.

关键词： Velocity level Acceleration level Torque level Bi-criteria quadratic program Redundancy resolution

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Northeastern Mathematical Journal 2004年第4期20卷 379-382页

作者：王德辉宋立新史宁中李荣华 SchoolofMathematics JilinUniversityChangchun130012 DepartmentofAppliedMathematics DalianInstituteofTechnologyDalian116023 DepartmentofMathematics NorthentNormalUniversityChangchun130021 不详

Suppose that the time series Xt satisfieswhere α0≥δ＞0,αi≥0 for i=1,2,…,q;βi,i=1,…,p, are real numbers; p and q are the order of the model. The sequence {ξt};（0,1） and is independent of {hs,s≤t} for fixed t. The above model is usually written as AR（p）-ARCH（q）.We consider stationary series AR（p）-ARCH（q） model and assume the stationary field is θ0. We express this statement asH1:α1≥α2…≥αq,β1≥β2≥…≥βp and we consider an order restricted testing problem, which is to testH0:α1=α2=…=αq,β1=β2=…=βpagainst H1-H0. We derive the likelihood ratio （LR） test statistic and its asymptotic distri-

关键词： AR(p)-ARCH(q) model ordered restriction maximum likelihood estimator asymptotic properties quadratic program