半无限数学规划的切割平面方法

M. Luhandjula, M. Ouanes
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引用次数: 1

摘要

许多情况,从工业到社会,再到经济和环境问题,都可以用半无限数学程序来描述。在本文中,切割平面方法更适合于标准非线性规划,并有充分的理由用于处理线性、凸和几何半无限规划。对于每种情况,讨论了计算方面并建立了收敛性陈述。为了说明问题,还提供了简单的数值例子。本文最后简要地比较了这里讨论的切面方法与其他现有方法,并强调了推动一个决策支持系统的必要性,该系统能够有效地帮助人们面对可以被表述为半无限数学规划的问题。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A CUTTING- PLANE APPROACH FOR SEMI- INFINITE MATHEMATICAL PROGRAMMING
Many situations ranging from industrial to social via economic and environmental problems may be cast into a Semi-infinite mathematical program. In this paper, the cutting-plane approach which lends itself better for standard non-linear programs is exploited with good reasons for grappling with linear, convex and geometric Semi-infinite programs. For each case, computational aspects are discussed and convergence statements established. Simple numerical examples are also provided for the sake of illustration. The paper ends by briefly comparing the cutting-plane approach discussed here with other existing approaches and by stressing the necessity of pushing forward a Decision Support System effectively capable for helping someone faced with a problem that can be formulated as a Semi-infinite mathematical program.
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