共查询到19条相似文献,搜索用时 93 毫秒
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《中国科学:数学》2020,(9)
可重复使用火箭技术是近五年来航天工程领域的焦点话题.以三自由度燃料最优控制问题为具体模型,本文研究火箭回收中的关键问题—动力下降制导问题的求解.由于此模型中包含非凸动力学约束(带空气阻力项)、非凸推力大小和方向控制约束等,直接求解方法难以满足工程上实时性的需求.为了消除非凸性带来的困难,本文通过无损凸化、时间离散化和线性化技术将问题转化为一类凸规化问题,即二阶锥规划问题进行求解.此外,为了避免传统的序列凸化策略在求解本文模型时的数值不稳定现象,本文提出一个新的两阶段序列凸化方法.数值结果表明所提方法仅需求解少量的凸规化问题,且拥有比单阶段方法更稳定和高效的数值表现. 相似文献
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约束非线性规划的神经网络算法 总被引:1,自引:0,他引:1
神经网络具有内在大规模并行运算和快速收敛特性,它在最优化技术上的运用近年来受到广泛的重视。本提出一个新的求解一般约束非线性规划的神经网络模型,它具有全局收敛性和广泛的适用性,是求解一般非线性规划问题的新工具。理论分析和模拟计算均表明了模型的有效性。 相似文献
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水火联合调度问题是电力系统中一类复杂的优化问题。合理安排调度周期内的水火电出力,确定一个最优发电计划,可以带来巨大的经济效益。在实际系统中,汽轮机调汽阀开启时出现的拔丝现象会使机组耗量特性产生阀点效应。忽略阀点效应,在一定程度上降低求解的精度。本文考虑带阀点效应的水火联合调度问题。该问题非凸非光滑,且带有非线性约束,直接使用确定性全局优化方法求解是相当困难的。本文使用高效的半定规划求解此问题。首先用耗量特性函数的初始周期代替其余有限的周期,并对其进行二次拉格朗日插值拟合。再通过引进0-1变量,得到整个耗量特性函数的近似,进而把问题松弛为半定规划模型。最后,采用凸规划应用软件包CVX求解一个仿真算例,得到一个近似全局最优解。 相似文献
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利用同伦方法求解非凸规划时,一般只能得到问题的K-K-T点.本文得到无界域上同伦方法求解非凸规划的几个收敛性定理,证明在一定条件下,通过构造合适的同伦方程,同伦算法收敛到问题的局部最优解. 相似文献
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凸二次规划问题逆问题的模型与解法 总被引:1,自引:0,他引:1
本文分别考虑带非负约束和不带大量负约束凸二次规划问题逆问题。首先得到各个逆问题的数学模型,然后对不同的模型给出不同的求解方法。 相似文献
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讨论非线性半定规划的四个专题, 包括半正定矩阵锥的变分分析、非凸半定规划问题的最优性条件、非凸半定规划问题的扰动分析和非凸半定规划问题的增广Lagrange方法. 相似文献
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讨论非线性半定规划的四个专题,包括半正定矩阵锥的变分分析、非凸半定规划问题的最优性条件、非凸半定规划问题的扰动分析和非凸半定规划问题的增广Lagrange方法. 相似文献
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组合同伦方法在无界域上的收敛性 总被引:3,自引:0,他引:3
组合同伦内点法由Feng等提出,是求解有界区域上的非凸数学规划的一种大范围收敛性方法,本文证明此算法适用于某些无界区域上的非凸数学规划问题。 相似文献
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本文提出了一个指数型凸化,凹化变换,并证明了单调非线性规划总能变换成相应的凹规划或凸规划.还证明了带某种类型线性或非线性约束的非线性规划在适当条件下能变换成单调非线性规划. 相似文献
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《Mathematical and Computer Modelling》1999,29(3):9-18
An artificial neural network is proposed in this paper for solving the linear complementarity problem. The new neural network is based on a reformulation of the linear complementarity problem into the unconstrained minimization problem. Our new neural network can be easily implemented on a circuit. On the theoretical aspect, we analyze the existence of the equilibrium points for our neural network. In addition, we prove that if the equilibrium point exists for the neural network, then any such equilibrium point is both asymptotically and bounded (Lagrange) stable for any initial state. Furthermore, linear programming and certain quadratical programming problems (not necessarily convex) can be also solved by the neural network. Simulation results on several problems including a nonconvex one are also reported. 相似文献
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A.R. Nazemi 《Communications in Nonlinear Science & Numerical Simulation》2012,17(4):1696-1705
This paper proposes a feedback neural network model for solving convex nonlinear programming (CNLP) problems. Under the condition that the objective function is convex and all constraint functions are strictly convex or that the objective function is strictly convex and the constraint function is convex, the proposed neural network is proved to be stable in the sense of Lyapunov and globally convergent to an exact optimal solution of the original problem. The validity and transient behavior of the neural network are demonstrated by using some examples. 相似文献
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Rodrigo Garcés Walter Gómez Florian Jarre 《Mathematical Methods of Operations Research》2011,74(1):77-92
The paper considers nonconvex quadratic semidefinite problems. This class arises, for instance, as subproblems in the sequential
semidefinite programming algorithm for solving general smooth nonlinear semidefinite problems. We extend locally the concept
of self-concordance to problems that satisfy a weak version of the second order sufficient optimality conditions. 相似文献
14.
Hoang Tuy 《Journal of Global Optimization》1992,2(1):21-40
We show the importance of exploiting the complementary convex structure for efficiently solving a wide class of specially structured nonconvex global optimization problems. Roughly speaking, a specific feature of these problems is that their nonconvex nucleus can be transformed into a complementary convex structure which can then be shifted to a subspace of much lower dimension than the original underlying space. This approach leads to quite efficient algorithms for many problems of practical interest, including linear and convex multiplicative programming problems, concave minimization problems with few nonlinear variables, bilevel linear optimization problems, etc... 相似文献
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In this paper, we are concerned with the development of parallel algorithms for solving some classes of nonconvex optimization problems. We present an introductory survey of parallel algorithms that have been used to solve structured problems (partially separable, and large-scale block structured problems), and algorithms based on parallel local searches for solving general nonconvex problems. Indefinite quadratic programming posynomial optimization, and the general global concave minimization problem can be solved using these approaches. In addition, for the minimum concave cost network flow problem, we are going to present new parallel search algorithms for large-scale problems. Computational results of an efficient implementation on a multi-transputer system will be presented. 相似文献
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Santiago Cerisola Jesus M. Latorre Andres Ramos 《European Journal of Operational Research》2012,218(3):687-697
In this paper we apply stochastic dual dynamic programming decomposition to a nonconvex multistage stochastic hydrothermal model where the nonlinear water head effects on production and the nonlinear dependence between the reservoir head and the reservoir volume are modeled. The nonconvex constraints that represent the production function of a hydro plant are approximated by McCormick envelopes. These constraints are split into smaller regions and the McCormick envelopes are used for each region. We use binary variables for this disjunctive programming approach and solve the problem with a decomposition method. We resort to a variant of the L-shaped method for solving the MIP subproblem with binary variables at any stage inside the stochastic dual dynamic programming algorithm. A realistic large-scale case study is presented. 相似文献
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In this paper, we present and evaluate a neural network model for solving a typical personnel-scheduling problem, i.e. an airport ground staff rostering problem. Personnel scheduling problems are widely found in servicing and manufacturing industries. The inherent complexity of personnel scheduling problems has normally resulted in the development of integer programming-based models and various heuristic solution procedures. The neural network approach has been admitted as a promising alternative to solving a variety of combinatorial optimization problems. While few works relate neural network to applications of personnel scheduling problems, there is great theoretical and practical value in exploring the potential of this area. In this paper, we introduce a neural network model following a relatively new modeling approach to solve a real rostering case. We show how to convert a mixed integer programming formulation to a neural network model. We also provide the experiment results comparing the neural network method with three popular heuristics, i.e. simulated annealing, Tabu search and genetic algorithm. The computational study reveals some potential of neural networks in solving personnel scheduling problems. 相似文献
18.
Steffen Rebennack Josef Kallrath Panos M. Pardalos 《Journal of Global Optimization》2009,43(2-3):277-297
We propose a decomposition algorithm for a special class of nonconvex mixed integer nonlinear programming problems which have an assignment constraint. If the assignment decisions are decoupled from the remaining constraints of the optimization problem, we propose to use a column enumeration approach. The master problem is a partitioning problem whose objective function coefficients are computed via subproblems. These problems can be linear, mixed integer linear, (non-)convex nonlinear, or mixed integer nonlinear. However, the important property of the subproblems is that we can compute their exact global optimum quickly. The proposed technique will be illustrated solving a cutting problem with optimum nonlinear programming subproblems. 相似文献