optimization第四講(編輯修改稿)
2024-11-17 05:44 本頁面
【文章內(nèi)容簡介】 f ’(x*) = 0 x* = 0 This implies that the following must hold: f ’(x*) ≥ 0 and x*f ’(x*) = 0 Thus: For a maximum: f ’(x*) ≤ 0 and x*f ’(x*) = 0 For a minimum: f ’(x*) ≥ 0 and x*f ’(x*) = 0,12,第十二頁，共二十九頁。,Combining results.,When we want to,we take,and derive the following KuhnTucker conditions:,13,第十三頁，共二十九頁。,Theorem 15.1,If f and g are concave and differentiable, and if Slater’s condition (there exists a point where g 0) is satisfied, then being able to solve this is necessary and sufficient for a solution to the problem! Thus: just find values of lambda and the x’s such that all the conditions are satisfied and you’re done! The book gives a formal proof for this result.,14,第十四頁，共二十九頁。,Back to the consumer problem,Again consider the consumer problem. Thus far, we have assumed that the consumer always chooses to consume his entire income. But this is not necessary! Actually, the problem should read like this:,The Lagrangean for this problem is:,Make sure to write the constraint in the correct manner!!!,15,第十五頁，共二十九頁。,Example,A consumer wants to maximize utility U(x1,x2) = x1189。 x2189。 subject to budg
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