# Question

Consider the following convex programming problem:

Maximize Z = 32x1 – x41 + 4x2 – x22,

Subject to

x21 + x22 ≤ 9 and

x1 ≥ 0, x2 ≥ 0.

(a) Apply the separable programming technique discussed at the end of Sec. 13.8, with x1 = 0, 1, 2, 3 and x2 = 0, 1, 2, 3 as the breakpoint of the piecewise linear functions, to formulate an approximate linear programming model for this problem.

Maximize Z = 32x1 – x41 + 4x2 – x22,

Subject to

x21 + x22 ≤ 9 and

x1 ≥ 0, x2 ≥ 0.

(a) Apply the separable programming technique discussed at the end of Sec. 13.8, with x1 = 0, 1, 2, 3 and x2 = 0, 1, 2, 3 as the breakpoint of the piecewise linear functions, to formulate an approximate linear programming model for this problem.

## Answer to relevant Questions

Reconsider the integer nonlinear programming model given in Prob. 11.3-9. (a) Show that the objective function is not concave. (b) Formulate an equivalent pure binary integer linear programming model for this problem as ...Consider the quadratic programming example presented in Sec. 13.7. Starting from the initial trial solution (x1, x2) = (5, 5), apply eight iterations of the Frank-Wolfe algorithm. Reconsider the linearly constrained convex programming model given in Prob. 13.9-9. Follow the instructions of parts (a), (b), and (c) of Prob. 13.9-10 for this model, except use (x1, x2) = (1/2, 1/2) as the initial trial ...Reconsider the convex programming model with an equality constraint given in Prob. 13.6-11. (a) If SUMT were to be applied to this model, what would be the unconstrained function P(x; r) to be minimized at each iteration? Consider the following problem: Maximize Z = 4x1 – x12 + 10x2 – x22, subject to x12 + 4x22 ≤ 16 and x1 ≥ 0, x2 ≥ 0. (a) Is this a convex programming problem? Answer yes or no, and then justify your answer. (b) Can ...Post your question

0