Powell's algorithm, starting from an initial point, performs a series
of line searches in one iteration.
The line search directions, except the last one, are all linearly independent.
The major advantage of Powell’s algorithm is that
the Hessian needs not be supplied, stored or manipulated.
However, this algorithm has a few drawbacks and is superseded by Zangwill’s algorithm.
For example, in an iteration, linear dependence can sometimes arise,
which may fail to find complete the set of linearly independent directions that span
even in the case of a convex quadratic problem.