可分解变分不等式的组合松弛法

IF 1.4 3区数学 Q3 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Optimization Methods & Software Pub Date : 1999-01-01 DOI:10.1080/10556789908805735

I. Konnov

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引用次数: 9

摘要

针对变分不等式问题，提出了一种基于组合、修正和推广不同松弛子梯度方法的迭代求解方法。对于某些结构化问题，这种方法导致分解方案。在弱假设条件下证明了该方法的收敛性。特别是，主映射不需要是单值的或单调的。

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A combined relaxation method for decomposable variational inequalities

An iterative method based on combining, modifying and generalizing different relaxation subgradient methods is proposed for solving variational inequality problems. For certain structured problems this method leads to a decomposition scheme. Convergence of the method is proved under weak assumptions. In particular, the main mapping need not be single-valued or monotone.

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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.