# Question

Use the KKT conditions to derive an optimal solution for each of the following problems.

(a) Maximize f(x) = x1 + 2x2 - x32,

subject to

x1 + x2 ≤ 1 and

x1 ≥ 0, x2 ≥ 0.

(b) Maximize f(x) 20x1 + 10x2,

Subject to

and

x1 ≥ 0, x2 ≥ 0.

(a) Maximize f(x) = x1 + 2x2 - x32,

subject to

x1 + x2 ≤ 1 and

x1 ≥ 0, x2 ≥ 0.

(b) Maximize f(x) 20x1 + 10x2,

Subject to

and

x1 ≥ 0, x2 ≥ 0.

## Answer to relevant Questions

What are the KKT conditions for nonlinear programming problems of the following form? Minimize f(x) Subject to gi(x) ≥ bi, for i = 1, 2, . . . ,m and x ≥ 0, 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. Consider the following quadratic programming problem: Maximize f (x) = 2x1 + 3x2 – x12 – x22, subject to x1 + x2 ≤ 2 and x1 ≥ 0, x2 ≥ 0. Reconsider the linearly constrained convex programming model given in Prob. 13.4-7. (a) Use the separable programming technique presented in Sec. 13.8 to formulate an approximate linear programming model for this problem. ...Reconsider 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.Post your question

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