PRECISE OPTIMIZATION USING RANGE ARITHMETIC

[摘要] In a recent paper by Aberth and Schaefer (1992), it was shown how an implementation of range arithmetic in the programming language C++ can serve as a basis for writing numerical programs which compute reliable answers. This arithmetic is more complex than floating-point arithmetic and is a form of interval arithmetic. Here we show how a search algorithm for local minima of smooth unconstrained functions can be adapted to range arithmetic in order to guarantee convergence and generate correct results.

[发布日期] 1994-08-30

[关键词] INTERVAL ARITHMETIC;RANGE ARITHMETIC;UNCONSTRAINED OPTIMIZATION;LEVENBERG-MARQUARDT METHODS