Review Questions 479(h)The solutions of all LP problems in the SLP method lie in the infeasible domain of
the original problem.
(i)The SLP method is applicable to both convex and nonconvex problems.
(j)The usable feasible directions can be generated using random numbers.
(k)The usable feasible direction makes an obtuse angle with the gradients of all the
constraints.
(l)If the starting point is feasible, all subsequent unconstrained minima will be feasible
in the exterior penalty function method.
(m)The interior penalty function method can be used to find a feasible starting point.
(n)The penalty parameterrkapproaches zero askapproaches infinity in the exterior
penalty function method.
(o)The design vector found through extrapolation can be used as a starting point for the
next unconstrained minimization in the interior penalty function method.7.2 Why is the SLP method called the cutting plane method?
7.3 How is the direction-finding problem solved in Zoutendijk’s method?
7.4 What is SUMT?
7.5 How is a parametric constraint handled in the interior penalty function method?
7.6 How can you identify an active constraint during numerical optimization?
7.7 Formulate the equivalent unconstrained objective function that can be used in random
search methods.
7.8 How is the perturbation method used as a convergence check?
7.9 How can you compute Lagrange multipliers during numerical optimization?7.10 What is the use of extrapolating the objective function in the penalty function approach?
7.11 Why is handling of equality constraints difficult in the penalty function methods?
7.12 What is the geometric interpretation of the reduced gradient?
7.13 Is the generalized reduced gradient zero at the optimum solution?
7.14 What is the relation between the sequential quadratic programming method and the
Lagrangian function?
7.15 Approximate the nonlinear functionf(X) as a linear function atX 0.
7.16 What is the limitation of the linear extended penalty function?
7.17 What is the difference between the interior and extended interior penalty function
methods?
7.18 What is the basic principle used in the augmented Lagrangian method?
7.19 When can you use the steepest descent direction as a usable feasible direction in
Zoutendijk’s method?
7.20 Construct the augmented Lagrangian function for a constrained optimization problem.