| 书目名称 | Infinite Programming | | 副标题 | Proceedings of an In | | 编辑 | Edward J. Anderson,Andrew B. Philpott | | 视频video | | | 丛书名称 | Lecture Notes in Economics and Mathematical Systems | | 图书封面 |  | | 描述 | Infinite programming may be defined as the study of mathematical programming problems in which the number of variables and the number of constraints are both possibly infinite. Many optimization problems in engineering, operations research, and economics have natural formul- ions as infinite programs. For example, the problem of Chebyshev approximation can be posed as a linear program with an infinite number of constraints. Formally, given continuous functions f,gl,g2, ••• ,gn on the interval [a,b], we can find the linear combination of the functions gl,g2, ... ,gn which is the best uniform approximation to f by choosing real numbers a,xl,x2, •.. ,x to n minimize a t€ [a,b]. This is an example of a semi-infinite program; the number of variables is finite and the number of constraints is infinite. An example of an infinite program in which the number of constraints and the number of variables are both infinite, is the well-known continuous linear program which can be formulated as follows. T minimize ~ c(t)Tx(t)dt t b(t) , subject to Bx(t) + fo Kx(s)ds x(t) .. 0, t € [0, T] • If x is regarded as a member of some infinite-dimensional vector space of functions, then this problem is a | | 出版日期 | Conference proceedings 1985 | | 关键词 | Programming; duality; economics; inequality; optimization | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-642-46564-2 | | isbn_softcover | 978-3-540-15996-4 | | isbn_ebook | 978-3-642-46564-2Series ISSN 0075-8442 Series E-ISSN 2196-9957 | | issn_series | 0075-8442 | | copyright | Springer-Verlag Berlin Heidelberg 1985 |
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发表于 2025-3-21 16:36:54
