Review Questions 3696.16 Why is Powell’s method called a pattern search method?
6.17 What are the roles of univariate and pattern moves in the Powell’s method?
6.18 What is univariate method?
6.19 Indicate a situation where a central difference formula is not as accurate as a forward
difference formula.
6.20 Why is a central difference formula more expensive than a forward or backward difference
formula in finding the gradient of a function?
6.21 What is the role of one-dimensional minimization methods in solving an unconstrained
minimization problem?
6.22 State possible convergence criteria that can be used in direct search methods.
6.23 Why is the steepest descent method not efficient in practice, although the directions used
are the best directions?
6.24 What are rank 1 and rank 2 updates?
6.25 How are the search directions generated in the Fletcher–Reeves method?
6.26 Give examples of methods that requiren^2 ,n, and 1 one-dimensional minimizations for
minimizing a quadratic innvariables.
6.27 What is the reason for possible divergence of Newton’s method?
6.28 Why is a conjugate directions method preferred in solving a general nonlinear problem?
6.29 What is the difference between Newton and quasi-Newton methods?
6.30 What is the basic difference between DFP and BFGS methods?
6.31 Why are the search directions reset to the steepest descent directions periodically in the
DFP method?
6.32 What is a metric? Why is the DFP method considered as a variable metric method?
6.33 Answer true or false:
(a)A conjugate gradient method can be called a conjugate directions method.
(b)A conjugate directions method can be called a conjugate gradient method.
(c)In the DFP method, the Hessian matrix is sequentially updated directly.
(d)In the BFGS method, the inverse of the Hessian matrix is sequentially updated.
(e)The Newton method requires the inversion of ann×nmatrix in each iteration.
(f)The DFP method requires the inversion of ann×nmatrix in each iteration.
(g)The steepest descent directions are the best possible directions.
(h)The central difference formula always gives a more accurate value of the gradient
than does the forward or backward difference formula.
(i)Powell’s method is a conjugate directions method.
(j)The univariate method is a conjugate directions method.