Exact Solutions to the Maxmin Problem max ||Ax|| Subject to ||Bx||<= 1
Mathematics(2024)
摘要
In this manuscript we provide an exact solution to the maxmin problem max
||Ax|| subject to ||Bx||<= 1, where A and B are real matrices. This problem
comes from a remodeling of max ||Ax|| subject to min ||Bx||, because the latter
problem has no solution. Our mathematical method comes from the Abstract
Operator Theory, whose strong machinery allows us to reduce the first problem
to max parallel to Cx parallel to subject to parallel to x parallel to <= 1,
which can be solved exactly by relying on supporting vectors. Finally, as
appendices, we provide two applications of our solution: first, we construct a
truly optimal minimum stored-energy Transcranian Magnetic Stimulation (TMS)
coil, and second, we find an optimal geolocation involving statistical
variables
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关键词
maxmin,supporting vector,matrix norm,tms coil,optimal geolocation
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