凸优化问题与平衡问题密切相关，本文对这二类问题进行研究。
In this thesis, we study two related problems: convex optimization problems and equilibrium problems.
系统的稳定界和反馈控制器可以通过求解一类线性矩阵不定式约束的凸优化问题得到。
The robust stable bound and the state feedback controller can be obtained by solving a class of convex optimization problems with LMI constraint.
本文研究了出现在系统与控制理论中的一些标准的、包含线性矩阵不等式的凸优化问题。
This paper discusses problems arising in system and control theory to a few standard convex optimization problems involving linear matrix inequality (LMI).
本文研究了出现在系统与控制理论中的一些标准的、包含线性矩阵不等式的凸优化问题。
In this paper, a new generalized gradient projection method with inexact line search is proposed for the nonlinear optimization problem with linear constraints.
通过求解一个线性矩阵不等式约束的凸优化问题，提出了最优化保性能控制律的设计方法。
Furthermore, a convex optimization problem with LMI constraints is formulated to design the optimal guaranteed cost controllers.
这两类算法是在ML算法基础上放松约束条件，将问题转化为可在多项式时间内解决的凸优化问题。
These two algorithms relax the constraints of ML algorithm and transform it into a convex problem which can be efficiently solved with a polynomial time.
系统与控制理论中的许多问题，都可转化为线性矩阵不等式约束的凸优化问题，从而简化其求解过程。
Many important problems of system and control theory can be reformulated as linear matrix inequality convex optimization problems, which is numerically tractable.
科学领域，工程领域和经济领域都涉及到很多复杂的、非线性的甚至非凸形式的最优化问题。
Many scientific, engineering and economic areas involve the optimization of complex, nonlinear and possibly non-convex problems.
在广义凸条件下，研究了带控制参量的向量优化问题。
Vector optimization problems with control parametra are considered under generalized convexity condition.
本文我们考虑求解凸约束优化问题的信赖域方法。
In this paper, we develop a trust region algorithm for convex constrained optimization problems.
本文在局部凸空间中对集值映射最优化问题引入超有效解的概念。
In this paper, we introduce a concept of super efficient solution of the optimization problem for a set-valued mapping.
采用线性矩阵不等式方法，将问题转化为一个线性凸优化算法。
The problem is reduced to a linear convex optimization algorithm via LMI approach.
接着，利用函数的上次微分构造了不可微向量优化问题（VP）的广义对偶模型，并且在适当的弱凸性条件下建立了弱对偶定理。
Finally, the generalized dual model of the problem (VP) is presented with the help of upper subdifferential of function, and a weak duality theorem is given.
应用已有的极点理论，优化相伴凸组合的界并改进整数规划问题的目标函数及变量的界。
Assuming knowledge of extreme points, we develop bounds for associated convex combinations and improve bounds on the integer programming problems objective function and variables.
由于采用的先验函数是非凸的并包含超验参数，一般的优化方法难以处理，采用动态后验模拟的方法可以很好地解决这些问题。
Due to the non-convex of the prior function and hyper-parameters, we use the dynamic posterior simulation rather than the general optimization methods to get reconstruction image.
然后，运用凸优化技术分析了该资源分配问题，并基于拉格朗日对偶法给出了一种子载波和功率最优分配算法。
Then, by use of multiple carrier system's frequency-sharing property and convex optimization, a subcarrier and power optimal allocation algorithm is proposed based on Lagrangian duality theory.
最后，利用择一性定理，获得了含不等式和等式约束的广义次似凸集值映射向量最优化问题的最优性条件。
Finally, the optimality conditions for vector optimization problems with set valued maps with equality and inequality constraints are obtained with it.
基于混沌神经网络模型可以有效地解决高维、离散、非凸的非线性约束优化问题。
The Chaotic neural network model can be used to solve many multi-dimensioned, discrete, non-convex, nonlinear constrained optimization problems.
在部分生成锥内部凸-锥-凸映射下，得到了既有等式约束又有不等式约束的向量优化问题弱有效解的最优性必要条件。
Under the conditions of Partial ic-convex like Maps, optimality necessary conditions of weak efficient solutions for vector optimization problems with equality and inequality constraints are obtained.
采用线性矩阵不等式技术，将问题转化为一线性凸优化算法，可得问题的全局最优解。
Using the linear matrix inequality (LMI) technique, the problem is converted into a linear convex optimization algorithm so that a global optimization solution is obtained. Finally.
本文旨在研究求解非凸约束优化问题的基于二阶导数的微分方程方法。
The aim of the dissertation is to study second order derivatives based differential equation approaches to nonconvex constrained optimization problems.
在凸规划理论中，通过KT条件，往往将约束最优化问题归结为一个混合互补问题来求解。
In convex programming theory, a constrained optimization problem, by KT conditions, is usually converted into a mixed nonlinear complementarity problem.
在此基础上，得到了向量目标函数既是似凸又是拟凸的多目标最优化问题的G-恰当有效解集是连通的结论。
On the conditions that vector objective function is like-convex and quasi-convex, we obtain the connectedness of G-proper efficient solution set of the multiobjective optimization problem.
可靠性指标；稳健；凸模型；优化问题；
本文基于不确定参量的凸集合描述，研究了结构和多学科系统的不确定性分析与考虑不确定因素的优化设计问题。
In this paper, the uncertainty analysis and design problems for structural and multidisciplinary system were investigated in detail base on a non-probabilistic approach that is convex model theory.
它将机器学习问题转化为求解最优化问题，并应用最优化理论构造算法来解决凸二次规划问题。
SVM transforms machine learning to solve an optimization problem, and to solve a convex quadratic programming problem by the optimization theory and method constructing algorithms.
该模型中的资源分配问题是一个非凸的非线性优化问题。
The problem of resource allocation in this scheme is a non-convex non-linear optimization problem.
论述了采用金属梯度性能材料优化拉杆类、压杆类、简支梁类、凸模类机械零件设计问题。
The design of mechanical parts, such as draw poles press poles, simple su stain girders and protruding models type parts may be optimized by use of metal gradient materials.
在此基础上，利用凸集的性质提出了一种求解响应集的支撑超平面法，它是利用响应集的支撑超平面将问题转化为求解一类优化问题的解。
The method is based on analytical results characterizing the solutions to a class of optimization problems that determine support hyperplanes of the response set.
在此基础上，利用凸集的性质提出了一种求解响应集的支撑超平面法，它是利用响应集的支撑超平面将问题转化为求解一类优化问题的解。
The method is based on analytical results characterizing the solutions to a class of optimization problems that determine support hyperplanes of the response set.
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