【作者】 张静文；

【导师】 刘德友；

【作者基本信息】 燕山大学 ， 概率论与数理统计， 2012， 硕士

【摘要】 全局优化问题是数学规划理论中重要而又困难的一个研究领域，它研究的是非线性函数在某个区域上全局最优点的特征和计算方法。由于目标函数通常不是凸函数，特定区域也有可能不是凸集，所以全局优化也可以称为非凸优化。全局最优的必要性条件是刻画一个解不是全局最优解的基本工具，而充分性条件是刻画一个解是全局最优解的基本工具。本文系统的讨论了时滞神经网络模型对于二次规划的全局最优性的建立、解的存在性、稳定性分析以及最优解的求法。首先本文讨论了时滞神经网络模型的来源，详尽的分析了全局优化的研究现状，给出了全局优化的确定性算法。随后研究了带有等式约束和不等式约束的二次规划的全局最优性，得到了系统的全局指数收敛，求得了收敛点为二次规划的最优解。证明了当M是半正定矩阵时，时滞神经网络模型全局收敛于退化的二次优化的最优解，同时也验证了稳定点一定为最优解。最后本文针对M是广义正定矩阵的一类新的带有不等式约束的不定二次规划问题，借助时滞神经网络模型，得到了系统解的存在性和唯一性。应用定性分析方法，构造恰当的李雅普诺夫函数，得到了该系统全局收敛于二次优化的最优解的充分条件，并在M是广义正定矩阵条件下，求得了系统的最优解。更多还原

【Abstract】 Mathematical programming problem of global optimization theory is an importantand difficult area of research. It is a nonlinear function of a region on the global optimalcharacteristics and methods of calculation. Since the objective function is usually notconvex function, specific regions are probably not convex; Therefore, global optimizationcan also be referred to as non-convex optimization. The need for global optimum solutionis not a condition that depicts a basic tool for the global optimal solution and sufficientcondition is portrayed a global optimum solution is a basic tool. This article discusses thesystem delay neural network model for quadratic programming, the establishment ofglobal optimality、existence of solutions、stability analysis and find the optimal solutionmethod.The first article discusses the sources of delay neural network model, detailedanalysis of the global optimization of research, gives the deterministic global optimizationalgorithm.Then studied with equality constraints and inequality constraints of the globaloptimum of quadratic programming, get the global exponential convergence of the system,Obtained a convergence point for the optimal solution of quadratic programming.Proved that when M is positive semi-definite matrix, delay neural network model onthe degradation of the global convergence of the optimal solution of quadraticoptimization, also verify that a stable point for the optimal solution.Finally, M is a generalized positive definite matrix for a new class of inequalityconstraints with indefinite quadratic programming problem; neural network model withdelay, system has been the existence of solutions and uniqueness. Application ofqualitative methods, construct an appropriate Lyapunov function, global convergence ofthe system has been optimized in the second sufficient condition for the optimal solution,and the matrix M is positive definite under the conditions of generalized, obtain theoptimal solution of the system.更多还原