Reconsider Prob. 13.2-9. Use the KKT conditions to check whether (x1, x2) = (1/√2, 1/ √2) is optimal.
Answer to relevant QuestionsReconsider the model given in Prob. 13.3-3. What are the KKT conditions for this model? Use these conditions to determine whether (x1, x2) = (0, 10) can be optimal. Consider the following nonlinear programming problem: Maximize Subject to x1 – x2 ≤ 2 and x1 ≥ 0, x2 ≥ 0. (a) Use the KKT conditions to demonstrate that (x1, x2) = (4, 2) is not optimal. Use the KKT conditions to determine whether (x1, x2, x3) = (1, 1, 1) can be optimal for the following problem: Minimize Z = 2x1 + x32 + x23, Subject to x21 + 2x22 + x23 ≥ 4 and x1 ≥ 0, x2 ≥ 0, x3 ≥ 0. Reconsider the first quadratic programming variation of the Wyndor Glass Co. problem presented in Sec. 13.2 (see Fig. 13.6). Analyze this problem by following the instructions of parts (a), (b), and (c) of Prob. 13.7-4. For each of the following cases, prove that the key property of separable programming given in Sec. 13.8 must hold. (a) The special case of separable programming where all the gi(x) are linear functions. (b) The general case ...
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