Operations Research
Mauro Gaggero Software ExercisesExercise 1
Solve the following linear programming problem using Lingo, Excel, and Matlab. min x1,x2∈R x1+ 2x2 x1+ x2 ≥2 x1− x2 ≤0 x1 ≥0 x2 ≥0 Exercise 2
Solve the following linear programming problem using Lingo, Excel, and Matlab. max x1,x2∈R x1− x2 −2x1+ x2 ≤2 x2≤1 x1≥0 x2≥0 Exercise 3
Use the Matlab Optimization Toolbox (function fminunc) to solve the following unconstrained nonlinear programming problem. Check when a minimum point is found (either local or global) and the number of iterations. Use as initial condition first x0
= −5 and then x0 = +1. min x∈R x4−23x2−18x + 40 Exercise 4
Use the Matlab Optimization Toolbox (function fminunc) to find the optimal point for the Rosenbrock banana function with a = 1. Use x0
1 = 5 and x 0 2 = 3 as initial condition. min x∈R2 a(x2− x21)2+ (x1−1)2 Exercise 5
Use the Matlab Optimization Toolbox (function fmincon) to find the optimal point for the Rosenbrock banana function with a = 1 and constraint x2
1≥2.
