Reconsider the linearly constrained convex programming model given in Prob. 13.6-12. Starting from the initial trial solution (x1, x2) = (0, 0), use one iteration of the Frank-Wolfe algorithm to obtain exactly the same solution you found in part (c) of Prob. 13.6-12, and then use a second iteration to verify that it is an optimal solution (because it is replicated exactly). Explain why exactly the same results would be obtained on these two iterations with any other trial solution.
Answer to relevant QuestionsReconsider the linearly constrained convex programming model given in Prob. 13.6-13. Starting from the initial trial solution (x1, x2, x3) = (0, 0, 0), apply two iterations of the Frank- Wolfe algorithm. Consider the following linearly constrained convex programming problem: Maximize f(x) = 3x1 x2 + 40x1 + 30x2 – 4x21 – x41 – 3x22 – x42, Subject to 4x1 + 3x2 ≤ 12 x1 + 2x2 ≤ 4 and x1 ≥ 0, x2 ≥ 0. Consider the following function: Show that f (x) is convex by expressing it as a sum of functions of one or two variables and then showing (see Appendix 2) that all these functions are convex. Consider the following nonconvex programming problem: Minimize f (x) = sin 3x1 + cos 3x2 + sin(x1 + x2), subject to x12 – 10x2 ≥ – 1 10x1 + x22 ≤ 100 and x1 ≥ 0, x2 ≥ 0. (a) If SUMT were applied to this problem, ...This case continues Case 3.4 involving an advertising campaign for Super Grain Corporation’s new breakfast cereal. The analysis requested for Case 3.4 leads to the application of linear programming. However, certain ...
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