Let S be convex set in n which contains no interior points of the nonnegative orthant n Then there exists a hyperplane with nonnegative normal p 0 (that is p 0, pi 0) such that pTx 0 for every x S ...

Let denote the positive orthant of is a convex set indeed cone with a nonempty ...

Let S be convex set in n which contains no interior points of the nonnegative orthant n+.

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Let S be convex set in ℜn which contains no interior points of the nonnegative orthant ℜn+. Then there exists a hyperplane with nonnegative normal p ≩ 0 (that is p ≠ 0, pi ≥ 0) such that pTx ≤ 0 for every x ∈ S.

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Foundations of Mathematical Economics

ISBN: 978-0262531924

1st edition

Authors: Michael Carter

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Question Posted: May 02, 2016 11:45 AM

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Let S be convex set in n that contains no interior points of the non positive orthant n-. Then there exists a hyperplane with nonnegative normal p 0 such that pTx 0 for every x S
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Let S be convex set in n which contains no interior points of the nonnegative orthant n+.

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Foundations of Mathematical Economics

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