Consider the linear programming problem (3.6) for a given basis B. Negate the equality constraint, so that is written −BxB − Nxn = −b. Associate Lagrange multipliers u with the equality constraint and...

Consider the linear programming problem (3.6) for a given basis B.

Negate the equality constraint, so that is written −BxB − Nxn = −b. Associate Lagrange multipliers u with the equality constraint and r with xN ≥ 0.

State the KKT conditions for an optimal basic solution (xB, 0). Why is the

regularity condition (i.e., the independence of constraint function gradients)

satisfied? Show that any solution satisfying the KKT conditions satisfies sufficient conditions for a global optimum. Verify that the KKT conditions are

identical with the LP optimality conditions in Theorem 3.1.