一类非线性抛物型边界控制问题的拉格朗日-牛顿方法*

IF 1.4 3区数学 Q3 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Optimization Methods & Software Pub Date : 1998-01-01 DOI:10.1080/10556789808805678

H. Goldberg, F. Tröltzscht

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引用次数: 25

摘要

研究了一类具有非线性边界条件的热方程最优控制问题。目标泛函由一个二次端点部分和一个二次正则化项组成。将关联最优性系统转化为!一个广义方程，求解最优控制问题的SQP方法与求解该广义方程的牛顿方法有关。通过证明最优性系统的强正则性，证明了五阶SQP方法的收敛性。在解释了理论结果的数值实现后，给出了一些高精度的测试实例

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On a lagrange — Newton method for a nonlinear parabolic boundary control problem ∗

An optimal control problem governed by the heat equation with nonlinear boundary conditions is considered. The objective functional consists of a quadratic terminal part aifid a quadratic regularization term. On transforming the associated optimality system to! a generalized equation, an SQP method for solving the optimal control problem is related to the Newton method for the generalized equation. In this way, the convergence of tfie SQP method is shown by proving the strong regularity of the optimality system. Aftjer explaining the numerical implementation of the theoretical results some high precision test examples are presented

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来源期刊

Optimization Methods & Software 工程技术-计算机：软件工程

CiteScore

4.50

自引率

0.00%

发文量

审稿时长

7 months

期刊介绍： Optimization Methods and Software publishes refereed papers on the latest developments in the theory and realization of optimization methods, with particular emphasis on the interface between software development and algorithm design. Topics include: Theory, implementation and performance evaluation of algorithms and computer codes for linear, nonlinear, discrete, stochastic optimization and optimal control. This includes in particular conic, semi-definite, mixed integer, network, non-smooth, multi-objective and global optimization by deterministic or nondeterministic algorithms. Algorithms and software for complementarity, variational inequalities and equilibrium problems, and also for solving inverse problems, systems of nonlinear equations and the numerical study of parameter dependent operators. Various aspects of efficient and user-friendly implementations: e.g. automatic differentiation, massively parallel optimization, distributed computing, on-line algorithms, error sensitivity and validity analysis, problem scaling, stopping criteria and symbolic numeric interfaces. Theoretical studies with clear potential for applications and successful applications of specially adapted optimization methods and software to fields like engineering, machine learning, data mining, economics, finance, biology, or medicine. These submissions should not consist solely of the straightforward use of standard optimization techniques.