The NLPC Nonlinear Optimization Solver |
At each iteration , the conjugate gradient (CONGRA), Newton-type (NEWTYP) and
quasi-Newton (QUANEW) optimization techniques use iterative line-search algorithms.
These algorithms try to optimize a quadratic or cubic approximation of some merit
function along the search direction
by computing an approximately optimal step
length
that is used as follows:
A line-search algorithm is an iterative process that optimizes a nonlinear function of
one variable within each iteration
of the main optimization
algorithm, which itself tries to optimize a quadratic approximation of the nonlinear
objective function
. Since the outside iteration process is based only on
the approximation of the objective function, the inside iteration of the line-search
algorithm does not have to be perfect. Usually the appropriate choice of
is
one that significantly reduces (in the case of minimization) the objective function value.
Criteria often used for termination of line-search algorithms are the Goldstein
conditions; see Fletcher (1987).
The line-search method in the NLPC solver is implemented as described in
Fletcher (1987).
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