# Question: Reconsider the integer nonlinear programming model given in Prob 11 3 9 a

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 follows. Apply the separable programming technique with the feasible integers as the breakpoints of the piecewise linear functions, so that the auxiliary variables are binary variables. Then add some linear programming constraints on these binary variables to enforce the special restriction of separable programming. (Note that the key property of separable programming does not hold for this problem because the objective function is not concave.)

(a) Show that the objective function is not concave.

(b) Formulate an equivalent pure binary integer linear programming model for this problem as follows. Apply the separable programming technique with the feasible integers as the breakpoints of the piecewise linear functions, so that the auxiliary variables are binary variables. Then add some linear programming constraints on these binary variables to enforce the special restriction of separable programming. (Note that the key property of separable programming does not hold for this problem because the objective function is not concave.)

## Relevant Questions

Reconsider the linearly constrained convex programming model given in Prob. 13.6-5. Starting from the initial trial solution (x1, x2) ≥ (0, 0), use one iteration of the Frank-Wolfe algorithm to obtain exactly the same ...Reconsider the quadratic programming model given in Prob. 13.7-4. Reconsider the model given in Prob. 13.3-3. (a) If SUMT were to be applied directly to this problem, what would be the unconstrained function P(x; r) to be minimized at each iteration? Consider the following nonconvex programming problem: Maximize f(x) = 1,000x – 400x2 + 40x3 – x4, Subject to x2 + x ≤ 500 and x ≥ 0. (a) Identify the feasible values for x. Obtain general expressions for the first ...Ever since the day she took her first economics class in high school, Lydia wondered about the financial practices of her parents. They worked very hard to earn enough money to live a comfortable middle-class life, but they ...Post your question