Return to the NLP of Exercise 17-46, and consider solving by active set Algorithm 17D starting from solution x102 = 10, 12.

(a) Demonstrate that the model is a quadratic program by deriving the c0,

c, Q, a112,

c, a142, b1,

c, b4, G, L, and E of general symmetric form 17.50 .

(b) State and solve as a system of linear equalities the active set optimality conditions 17.53 corresponding to initial solution x102.

(c) Determine the step l that would be applied to the direction resulting from part

(b), and compute the new point x112.

(d) Verify by forming and solving the optimality conditions 17.53 corresponding to x112 that no further progress can be made if all inequalities active at x112 of part (c)

are included in the active set S.

(e) Use the results of part

(d) to show which active constraint should be dropped from S.

(f) Begin from part

(e) and complete the solution of this quadratic program.

(g) Graph your progress in a plot of the feasible 1x1, x22.

(h) Compare the evolution of active set Algorithm 17D in part (g) with corresponding reduced gradient Algorithm 17C computations in Exercise 17-47.