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Applications of Interval Arithmetic in Signomial Programming

Louis Joseph ManciniStanford University. Systems Optimization Laboratory

出版	Stanford University, 1975
URL	http://books.google.com.hk/books?id=TdEEAAAAIAAJ&hl=&source=gbs_api

註釋

Many problems in engineering design can be found formulated as a nonlinear program where a criterion function of the design variables is minimized, or maximized, subject to certain inequality and equality constraints which define the problem. Such a formulation allows the engineer to use optimization theory and numerical algorithms to find the best design, or global solution, among the possibily infinite number of reasible designs. However, optimization methods are guaranteed to yield the global solution only if the nonlinear program has a certain structure; and in many cases only a solution which is guaranteed to be locally optimal can be obtained. The problem of multiple local solutions in nonlinear programs is of major concern to both the engineer and operations researcher. If all the functions in the nonlinear program are sums of power functions, then the nonlinear program is a signomial program. All the methods presented here use interval arithmetic, a generalization of ordinary arithmetic in which the basic elements are closed intervals of the real line. This study brings interval arithmetic and signomial programming together.