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# include "cppad_ipopt_nlp.hpp"
cppad_ipopt_solution solution;
cppad_ipopt_nlp cppad_nlp(
n, m, x_i, x_l, x_u, g_l, g_u, &fg_info, &solution
)
export LD_LIBRARY_PATH=$LD_LIBRARY_PATH:ipopt_library_pathscppad_ipopt_nlp is used to solve nonlinear programming
problems of the form
@[@
\begin{array}{rll}
{\rm minimize} & f(x)
\\
{\rm subject \; to} & g^l \leq g(x) \leq g^u
\\
& x^l \leq x \leq x^u
\end{array}
@]@
This is done using
Ipopt
optimizer and
CppAD
Algorithmic Differentiation package.
cppad_ipopt namespace
(not the CppAD namespace).
For example; SizeVector
below
actually denotes the type cppad_ipopt::SizeVector.
LD_LIBRARY_PATH.
You can determine the directory you need to add using the command
pkg-config ipopt --libs
%
The output will have the following form
-Ldir -lipopt
LD_LIBRARY_PATH%; e.g.,
export LD_LIBRARY_PATH="dir:$LD_LIBRARY_PATH"
index vector
as a vector of non-negative integers
for which none of the values are equal; i.e.,
it is both a vector and a set.
If @(@
I
@)@ is an index vector @(@
|I|
@)@ is used to denote the
number of elements in @(@
I
@)@ and @(@
\| I \|
@)@ is used
to denote the value of the maximum element in @(@
I
@)@.
SizeVector
is defined by the
cppad_ipopt_nlp.hpp
include file to be a
SimpleVector
class with elements of type
size_t.
NumberVector
is defined by the
cppad_ipopt_nlp.hpp
include file to be a
SimpleVector
class with elements of type
Ipopt::Number.
ADNumber
is defined by the
cppad_ipopt_nlp.hpp
include file to be a
an AD type that can be used to compute derivatives.
ADVector
is defined by the
cppad_ipopt_nlp.hpp
include file to be a
SimpleVector
class with elements of type
ADNumber.
n
has prototype
size_t n
m
has prototype
size_t m
x_i
has prototype
const NumberVector& x_i
x_l
has prototype
const NumberVector& x_l
x_u
has prototype
const NumberVector& x_u
g_l
has prototype
const NumberVector& g_l
g_u
has prototype
const NumberVector& g_u
fg_info
has prototype
FG_info fg_info
FG_info
is derived from the
base class cppad_ipopt_fg_info.
Certain virtual member functions of
fg_info
are used to
compute the value of @(@
fg(x)
@)@.
The specifications for these member functions are given below:
virtual size_t cppad_ipopt_fg_info::number_functions(void)
K
has type size_t, the syntax
K = fg_info.number_functions()
K
to the number of functions used in the
representation of @(@
fg(x)
@)@; i.e., @(@
K
@)@ in
the representation
above.
cppad_ipopt_fg_info implementation of this function
corresponds to the simple representation mentioned above; i.e.
K = 1
.
virtual ADVector cppad_ipopt_fg_info::eval_r(size_t k, const ADVector& u) = 0;
FG_info
.
k
in @(@
\{0 , \ldots , K-1 \}
@)@ has type size_t,
u
is an ADVector of size
q(k)
and
r
is an ADVector of size
p(k)
the syntax
r = fg_info.eval_r(k, u)
r
to the vector @(@
r_k (u)
@)@.
virtual bool cppad_ipopt_fg_info::retape(size_t k)
k
in @(@
\{0 , \ldots , K-1 \}
@)@ has type size_t,
and
retape
has type bool,
the syntax
retape = fg_info.retape(k)
retape
to true or false.
If
retape
is true,
cppad_ipopt_nlp will retape the operation sequence
corresponding to @(@
r_k (u)
@)@ for
every value of
u
.
An cppad_ipopt_nlp object
should use much less memory and run faster if
retape
is false.
You can test both the true and false cases to make sure
the operation sequence does not depend on
u
.
cppad_ipopt_fg_info implementation of this function
sets
retape
to true
(while slower it is also safer to always retape).
virtual size_t cppad_ipopt_fg_info::domain_size(size_t k)
k
in @(@
\{0 , \ldots , K-1 \}
@)@ has type size_t,
and
q
has type size_t, the syntax
q = fg_info.domain_size(k)
q
to the dimension of the domain space for @(@
r_k (u)
@)@;
i.e., @(@
q(k)
@)@ in
the representation
above.
cppad_ipopt_h_base implementation of this function
corresponds to the simple representation mentioned above; i.e.,
@(@
q = n
@)@.
virtual size_t cppad_ipopt_fg_info::range_size(size_t k)
k
in @(@
\{0 , \ldots , K-1 \}
@)@ has type size_t,
and
p
has type size_t, the syntax
p = fg_info.range_size(k)
p
to the dimension of the range space for @(@
r_k (u)
@)@;
i.e., @(@
p(k)
@)@ in
the representation
above.
cppad_ipopt_h_base implementation of this function
corresponds to the simple representation mentioned above; i.e.,
@(@
p = m+1
@)@.
virtual size_t cppad_ipopt_fg_info::number_terms(size_t k)
k
in @(@
\{0 , \ldots , K-1 \}
@)@ has type size_t,
and
L
has type size_t, the syntax
L = fg_info.number_terms(k)
L
to the number of terms in representation
for this value of
k
;
i.e., @(@
L(k)
@)@ in
the representation
above.
cppad_ipopt_h_base implementation of this function
corresponds to the simple representation mentioned above; i.e.,
@(@
L = 1
@)@.
virtual void cppad_ipopt_fg_info::index(
size_t k, size_t ell, SizeVector& I, SizeVector& J
)
k
size_t
and is a value between zero and @(@
K-1
@)@ inclusive.
The argument
ell
size_t
and is a value between zero and @(@
L(k)-1
@)@ inclusive.
The argument
I
size_t and size greater than or equal to @(@
p(k)
@)@.
The input value of the elements of
I
does not matter.
The output value of
the first @(@
p(k)
@)@ elements of
I
must be the corresponding elements of @(@
I_{k,ell}
@)@
in the representation
above.
The argument
J
size_t and size greater than or equal to @(@
q(k)
@)@.
The input value of the elements of
J
does not matter.
The output value of
the first @(@
q(k)
@)@ elements of
J
must be the corresponding elements of @(@
J_{k,ell}
@)@
in the representation
above.
cppad_ipopt_h_base implementation of this function
corresponds to the simple representation mentioned above; i.e.,
for @(@
i = 0 , \ldots , m
@)@,
I[i] = i
,
and for @(@
j = 0 , \ldots , n-1
@)@,
J[j] = j
.
solution
contains
the following information:
status
field of
solution
has prototype
cppad_ipopt_solution::solution_status solution.status
status
| Meaning |
| not_defined |
The optimizer did not return a final status to this cppad_ipopt_nlp
object.
|
| unknown |
The status returned by the optimizer is not defined in the Ipopt
documentation for finalize_solution.
|
| success | Algorithm terminated successfully at a point satisfying the convergence tolerances (see Ipopt options). |
| maxiter_exceeded | The maximum number of iterations was exceeded (see Ipopt options). |
| stop_at_tiny_step | Algorithm terminated because progress was very slow. |
| stop_at_acceptable_point | Algorithm stopped at a point that was converged, not to the 'desired' tolerances, but to 'acceptable' tolerances (see Ipopt options). |
| local_infeasibility | Algorithm converged to a non-feasible point (problem may have no solution). |
| user_requested_stop | This return value should not happen. |
| diverging_iterates | It the iterates are diverging. |
| restoration_failure | Restoration phase failed, algorithm doesn't know how to proceed. |
| error_in_step_computation | An unrecoverable error occurred while Ipopt tried to compute the search direction. |
| invalid_number_detected |
Algorithm received an invalid number (such as nan or inf)
from the users function
fg_info.eval
or from the CppAD evaluations
of its derivatives
(see the Ipopt option check_derivatives_for_naninf).
|
| internal_error | An unknown Ipopt internal error occurred. Contact the Ipopt authors through the mailing list. |
x field of
solution
has prototype
NumberVector solution.x
z_l field of
solution
has prototype
NumberVector solution.z_l
z_u field of
solution
has prototype
NumberVector solution.z_u
g field of
solution
has prototype
NumberVector solution.g
lambda field of
solution
has prototype
NumberVector solution.lambda
obj_value field of
solution
has prototype
Number solution.obj_value