多目标规划中的LFS函数

IF 0.6 4区数学 Q4 MATHEMATICS, APPLIED

Applications of Mathematics Pub Date : 1996-01-01 DOI:10.21136/AM.1996.134331

L. Neralić, S. Zlobec

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引用次数: 4

摘要

研究了具有非光滑函数的多目标凸规划中，有效(Pareto)解集与适当有效解集重合的条件。特别是当所有函数都具有局部平面(LFS)时，这种情况就会发生。在没有LFS性质的情况下，这两个集合通常是不同的，对于具有三个或更多变量的问题，有效解的特征采用渐近形式。该结果应用于公路建设中的一个问题，该问题同时优化了需要去除的污垢数量和地形形状的均匀平整度。

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LFS functions in multi-objective programming

We find conditions, in multi-objective convex programming with nonsmooth functions, when the sets of efficient (Pareto) and properly efficient solutions coincide. This occurs, in particular, when all functions have locally flat surfaces (LFS). In the absence of the LFS property the two sets are generally different and the characterizations of efficient solutions assume an asymptotic form for problems with three or more variables. The results are applied to a problem in highway construction, where the quantity of dirt to be removed and the uniform smoothness of the shape of a terrain are optimized simultaneously.

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来源期刊

Applications of Mathematics 数学-应用数学

CiteScore

1.50

自引率

0.00%

发文量

审稿时长

3.0 months

期刊介绍： Applications of Mathematics publishes original high quality research papers that are directed towards applications of mathematical methods in various branches of science and engineering. The main topics covered include: - Mechanics of Solids; - Fluid Mechanics; - Electrical Engineering; - Solutions of Differential and Integral Equations; - Mathematical Physics; - Optimization; - Probability Mathematical Statistics. The journal is of interest to a wide audience of mathematicians, scientists and engineers concerned with the development of scientific computing, mathematical statistics and applicable mathematics in general.