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LOCAL MINIMIZER OF A NONCONVEX quadratic-programming problem

COMPUTING 1990年第3期45卷 283-289页

作者： MRAZ, F 1. Pedagogical Faculty Jeronymova 10 CS-37115 ?. Budějovice Czechoslovakia

A modified Beale's algorithm is described which computes the local minimizer of any quadratic objective function subject to linear constraints. Some extensions are given, first of all the possibility of movement t... 详细信息

关键词： 90C20 quadratic programming problem local minimizer

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On a quadratic programming problem involving distances in trees

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ANNALS OF OPERATIONS RESEARCH 2016年第1-2期243卷 365-373页

作者： Bapat, R. B. Neogy, S. K. Indian Stat Inst Theoret Stat & Math 7 SJS Sansanwal Marg New Delhi 110016 India Indian Stat Inst Stat Qual Control & Operat Res Unit 7 SJS Sansanwal Marg New Delhi 110016 India

Let T be a tree and let D be the distance matrix of the tree. The problem of finding the maximum of x' Dx subject to x being a nonnegative vector with sum one occurs in many different contexts. These include some classical work on the transfinite diameter of a finite metric space, equilibrium points of symmetric bimatrix games and maximizing weighted average distance in graphs. We show that the problem can be converted into a strictly convex quadratic programming problem and hence it can be solved in polynomial time.

关键词： Tree Distance matrix quadratic programming problem Finite metric space Symmetric bimatrix game Polynomial time Lemke's algorithm

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Regular Splitting and Potential Reduction Method for Solving quadratic programming problem with Box Constraints

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Journal of Computational Mathematics 2002年第6期20卷 643-652页

作者： Zi-Luan Wei(Institute of Computational Mathematics and Scientific / Engineering Computing, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, P.O. Box 2719, Beijing, 100080) Institute of Computational Mathematics and Scientific / Engineering Computing Academy of Mathematics and System Sciences Chinese Academy of Sciences P.O. Box 2719 北京 100080

Presents a regular splitting and potential reduction method for solving a quadratic programming problem with box constraints. Discussion on the regular splitting and potential reduction algorithm; Complexity analysis ... 详细信息

关键词： quadratic programming problem regular splitting potential reduction algorithm complexity analysis

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Stability analysis of proportional delayed projection neural network for quadratic programming problem

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International Journal of Biomathematics 2023年第1期16卷 235-259页

作者： Xiehui Song Liqun Zhou Yu Wang Shiru Zhang Yuji Zhang School of Mathematics Science Tianjin Normal University Tianjin 300387 P.R.China

At present,projection neural network(PNN)with bounded time delay has been widely used for solving convex quadratic programming problem(QPP).However,there is little research concerning PNN with unbounded time *** this paper,we propose the proportional delayed PNN to solve QPP with equality *** utilizing homeo morphism mapping principle,we prove the proportional delayed PNN exists with unique equilibrium point which is the optimal solution of ***,delay-dependent criteria about global exponential stability(GES)and global polynomial stability(GPS)are also acquired by applying the method of variation of constants and inequality *** the other hand,when proportional delay factor q is equal to 1,the proportional delayed PNN becomes the one without time delay which still can be utilized for solving *** in most situations,q is not equal to 1,and time delay is unpredictable and may be unbounded in the actual neural network,which causes instability of ***,it is necessary to consider proportional delayed PNN.A numerical example demonstrates that,compared with the proportional delayed Lagrange neural network,the proportional delayed PNN is faster in terms of convergence *** possible reason is that appropriate parameters make the model converge to the equilibrium point along the direction of gradient descent.

关键词： quadratic programming problem proportional delay neural networks(NNs) exponential stability polynomial stability

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On active-set methods for the quadratic programming problem

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COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS 2012年第4期52卷 512-523页

作者： Daryina, A. N. Izmailov, A. F. Russian Acad Sci Dorodnicyn Comp Ctr Moscow 119333 Russia Moscow MV Lomonosov State Univ Fac Computat Math & Cybernet Moscow 119992 Russia

The active-set Newton method developed earlier by the authors for mixed complementarity problems is applied to solving the quadratic programming problem with a positive definite matrix of the objective function. A theoretical justification is given to the fact that the method is guaranteed to find the exact solution in a finite number of steps. Numerical results indicate that this approach is competitive with other available methods for quadratic programming problems.

关键词： quadratic programming problem active-set method semismooth Newton method Fisher-Burmeister function

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An algorithm to solve multi-objective integer quadratic programming problem

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ANNALS OF OPERATIONS RESEARCH 2024年第1-3期332卷 433-459页

作者： Kushwah, Prerna Sharma, Vikas TIET Sch Math Patiala India

The multi-objective integer programming problem often occurs in multi-criteria decision making situations, where the decision variables are integers. In the present paper, we have discussed an algorithm for finding all efficient solutions of a multi-objective integer quadratic programming problem. The proposed algorithm is based on the aspect that efficient solutions of a multi-objective integer quadratic programming problem can be obtained by enumerating ranked solutions of an integer quadratic programming problem. For determining ranked solutions of an integer quadratic programming problem, we have constructed a related integer linear programming problem and from ranked solutions of this integer linear programming problem, ranked solutions of the original integer quadratic programming problem are generated. Theoretically, we have shown that the developed method generates the set of all efficient solutions in a finite number of steps, and numerically we have elaborated the working of our algorithm and compared our results with existing algorithms. Further, we have analyzed that the developed method is efficient for solving a multi-objective integer quadratic programming problem with a large number of constraints, variables and objectives.

关键词： Efficient set Integer programming problem Multiple objective programming problem quadratic programming problem

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A SPLITTING METHOD FOR quadratic programming problem

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Acta Mathematicae Applicatae Sinica 2001年第3期17卷 366-374页

作者：魏紫銮 Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing China

A matrix splitting method is presented for minimizing a quadratic programming (QP) problem, and a general algorithm is designed to solve the QP problem and generates a sequence of iterative points. We prove that the sequence generated by the algorithm converges to the optimal solution and has an R-linear rate of convergence if the QP problem is strictly convex and nondegenerate, and that every accumulation point of the sequence generated by the general algorithm is a KKT point of the original problem under the hypothesis that the value of the objective function is bounded below on the constrained region, and that the sequence converges to a KKT point if the problem is nondegenerate and the constrained region is bounded.

关键词： quadratic programming problem matrix splitting method R-linear rate of convergence

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Generalized quadratic programming problem with Interval Uncertainty

Generalized Quadratic Programming Problem with Interval Unce...

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IEEE International Conference on Fuzzy Systems (FUZZ)

作者： Kumar, P. Panda, G. Gupta, U. C. Indian Inst Technol Dept Math Kharagpur 721302 W Bengal India

ISBN: (纸本)9781479900206

In this paper, a quadratic programming model is considered, wherein all parameters and decision variables take values in intervals. Existence of optimal solution for this model with certain acceptable level is justified and a methodology is proposed to derive such a solution. Finally, the theoretical development is illustrated by means of an example of portfolio selection.

关键词： quadratic programming problem interval order relation portfolio selection Risk

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Predictive Control with Particular Modifications in quadratic programming problem 20

Predictive Control with Particular Modifications in Quadrati...

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20th International Conference on Process Control (PC)

作者： Barot, Tomas Kubalcik, Marek Tomas Bata Univ Zlin Fac Appl Informat Dept Proc Control Nam TG Masaryka 5555 Zlin 76001 Czech Republic

ISBN: (纸本)9781467366274

Various kinds of processes can be controlled using predictive control. In certain cases of predictive control of fast-dynamics processes, a predictive control algorithm may not be feasible within the sampling-period time. These situations occur when requirements on control are more complex. For higher horizons and many constraints on control variables, the overloading of the sampling period can occur. In this contribution, the original algorithm of the quadratic programming is modified and verified by simulation and time analysis. For purposes of reducing of the algorithm complexity, a method based on the particular modifications in a solution of the quadratic programming problem is presented.

关键词： Predictive Control Constraints Processes with Fast Dynamics Optimization quadratic programming problem Time Analysis

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A Newton-Type Method for quadratic programming problem and Variational Equilibrium problem 13

A Newton-Type Method for Quadratic Programming Problem and V...

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13th International Symposium on Intelligent Systems (INTELS)

作者： Daryina, A. N. Andrianov, K. Yu. Kulakov, B. B. Russian Acad Sci Fed Res Ctr Comp Sci & Control Vavilov Str 442 Moscow 119333 Russia RUDN Univ Miklukho Maklaya Str 6 Moscow 117198 Russia

The active-set Newton method developed earlier by the author and her supervisor for mixed complementarity problems is applied to solving the quadratic programming problem with a positive definite matrix of the objective function and for variational equilibrium problem. A theoretical justification is given to the fact that the method is guaranteed to find the exact solution in a finite number of steps. Numerical results indicate that this approach is competitive with other available methods as for quadratic programming problems and for variational equilibrium problem. (C) 2019 The Authors. Published by Elsevier B.V.

关键词： Newton-type method quadratic programming problem variational equilibrium problem error bound semistability

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