NLPInterfacePack::ExampleNLPBanded Class Reference

Simple scalable serial NLP subclass. More...

#include <NLPInterfacePack_ExampleNLPBanded.hpp>

Inheritance diagram for NLPInterfacePack::ExampleNLPBanded:


Constructors / initializers
	ExampleNLPBanded (size_type nD, size_type nI, size_type bw=1, size_type mU=0, size_type mI=0, value_type xo=0.1, value_type xDl=-NLP::infinite_bound(), value_type xDu=+NLP::infinite_bound(), value_type xIl=-NLP::infinite_bound(), value_type xIu=+NLP::infinite_bound(), value_type hl=-NLP::infinite_bound(), value_type hu=+NLP::infinite_bound(), bool nlp_selects_basis=false, value_type diag_scal=10.0, value_type diag_vary=1.0, bool sym_basis=false, value_type f_offset=0.0, value_type co=0.0, bool ignore_constraints=false)
	Constructor.
Overridden public members from NLP
void	initialize (bool test_setup)

bool	is_initialized () const

value_type	max_var_bounds_viol () const

Overridden from NLPVarReductPerm
bool	nlp_selects_basis () const

Overridden protected methods from NLPSerialPreprocess
bool	imp_nlp_has_changed () const

size_type	imp_n_orig () const

size_type	imp_m_orig () const

size_type	imp_mI_orig () const

const DVectorSlice	imp_xinit_orig () const

bool	imp_has_var_bounds () const

const DVectorSlice	imp_xl_orig () const

const DVectorSlice	imp_xu_orig () const

const DVectorSlice	imp_hl_orig () const

const DVectorSlice	imp_hu_orig () const

void	imp_calc_f_orig (const DVectorSlice &x_full, bool newx, const ZeroOrderInfoSerial &zero_order_info) const

void	imp_calc_c_orig (const DVectorSlice &x_full, bool newx, const ZeroOrderInfoSerial &zero_order_info) const

void	imp_calc_h_orig (const DVectorSlice &x_full, bool newx, const ZeroOrderInfoSerial &zero_order_info) const

void	imp_calc_Gf_orig (const DVectorSlice &x_full, bool newx, const ObjGradInfoSerial &obj_grad_info) const

bool	imp_get_next_basis (IVector var_perm_full, IVector equ_perm_full, size_type rank_full, size_type rank)

void	imp_report_orig_final_solution (const DVectorSlice &x_orig, const DVectorSlice lambda_orig, const DVectorSlice lambdaI_orig, const DVectorSlice *nu_orig, bool is_optimal) const

Overridden protected methods from NLPSerialPreprocessExplJac
size_type	imp_Gc_nz_orig () const

size_type	imp_Gh_nz_orig () const

void	imp_calc_Gc_orig (const DVectorSlice &x_full, bool newx, const FirstOrderExplInfo &first_order_expl_info) const

void	imp_calc_Gh_orig (const DVectorSlice &x_full, bool newx, const FirstOrderExplInfo &first_order_expl_info) const

Detailed Description

Simple scalable serial NLP subclass.

This example NLP is a scalable problem where the basis of the jacobian of the equality constraints is a banded (band width = bw) symmetric positive definite matrix. Both the number of dependnet and independent variables can be varied.

To setup this NLP, the client specifies:

nD : the number of dependent variables
nI : the number of independent variables (nI <= nD)
bw : the band width (defined as the number of diagonals, including the center diagonal i==j that have non-zero element)
mU : the number of undecomposed dependent constraints
mI : the number of general constraints
diag_scal : Constant scaling factor for the diagonal elements
diag_vary : The scaling factor for the diagonal elements (to produce illconditioning) between the largets and the smallest.
sym_basis : True if the basis (selected by the NLP) is symmetric or not.

This NLP is defined as:


    min    f(x) = (1/2) * sum( x(i)^2, for i = 1..n )
    s.t.
           c(j) = ( ds(j)*x(j)                                 \
                    - sum( 3/(k)*x(j-k), k=1...klu(j) )        |
                    - sum( fu/(k)*x(j+k), k=1...kuu(j) )       | for j  = 1...nD
                   ) * (x(nD+q(j)) + 1)^2                      |
                   + co(j) == 0                                /

            c(nD+jU) = c(jU) + co(nD+jU)  == 0                 } for jU = 1...mU

            hl(jI) <= x(jI) - x(nD+q(jI)) <= hu(jI)            } for jI = 1...mI

            xl(i) <= x(i) <= xu(i)                             } for i  = 1...n

    where:

        n = nD + nI

        m = nD + mU

        mI = mI

        ds(j) = diag_scal * ( (diag_vary - 1)/(nD -1) * (j - 1) + 1 )

             / 3  : if sym_basis = true
        fu = |
             \ 6  : if sym_basis = false

                                 / 2  : if floor((j-1)/nI) < nD % nI
        q(j) = floor((j-1)/nI) + |
                                 \ 1  : if floor((j-1)/nI) >= nD % nI

                                                                  
                  / bw-1 : if j - bw >= 0                         \
        klu(j) =  |                                               |
                  \ j-1  : if j - bw <= 1                         |
                                                                  | for j=1...nD
                  / bw-1 : if j + bw-1 <= nD                      |
        kuu(j) =  |                                               |
                  \ nD-j : if j - bw <= 1                         /

In the above formuation, the sums are not computed if the upper bounds on k are zero. The term co(j) is an adjustable term that can be used to manipulate the solution. Note that if co(nD+jI) != 0 above, then the undecomposed dependent equality constraints are inconsistent with the decomposed equalities and therefore the NLP is infeasible. An infeasible NLP can also be created by manipulating xl(i), xu(i), hl(jI), hu(jI) and co(j).

For the above NLP, the Jacobian of the decomposed equalities has Jacobian elements:

    
                      /  -3/(j-i) * (x(nD+q(j)) + 1)^2         : i - klu(i) <= j < i
                      |
                      |  ds(j) * (x(nD+q(j)) + 1)^2            : i == j
   d(c(j))/d(x(i)) =  |
                      |  -3/(i-j) * (x(nD+q(j)) + 1)^2         : i < j <= i + kuu(i)
                      |
                      |  2 * (c(j) - co(j)) / (x(nD+q(j)) + 1) : i == nD + q
                      | 
                      \  0                                     : otherwise
                      
                      , for j = 1...nD, i = 1...nD+nI

The above definition shows that for the independent variables, the Jacobian elements are written in terms of the constraint c(j). This fact is exploited in the computational routines when this->multi_calc() == true.

For nD == 7, nI == 2, bw = 2 with floor(nD/nI) = 3 and nD % nI = 1, the Jacobian Gc' looks like:


   1 | x  x                 x    |
   2 | x  x  x              x    |
   3 |    x  x  x           x    |
   4 |       x  x  x        x    |
   5 |          x  x  x        x |
   6 |             x  x  x     x |
   7 |                x  x     x |
       -  -  -  -  -  -  -  -  -
       1  2  3  4  5  6  7  8  9

ToDo: Finish documentation!

Definition at line 143 of file NLPInterfacePack_ExampleNLPBanded.hpp.

Constructor & Destructor Documentation

NLPInterfacePack::ExampleNLPBanded::ExampleNLPBanded ( size_type nD,

size_type nI,

size_type bw = 1,

size_type mU = 0,

size_type mI = 0,

value_type xo = 0.1,

value_type xDl = -NLP::infinite_bound(),

value_type xDu = +NLP::infinite_bound(),

value_type xIl = -NLP::infinite_bound(),

value_type xIu = +NLP::infinite_bound(),

value_type hl = -NLP::infinite_bound(),

value_type hu = +NLP::infinite_bound(),

bool nlp_selects_basis = false,

value_type diag_scal = 10.0,

value_type diag_vary = 1.0,

bool sym_basis = false,

value_type f_offset = 0.0,

value_type co = 0.0,

bool ignore_constraints = false

)

Constructor.
ToDo: Finish documentation!
Definition at line 40 of file NLPInterfacePack_ExampleNLPBanded.cpp.

Member Function Documentation

void NLPInterfacePack::ExampleNLPBanded::initialize ( bool test_setup ) [virtual]

Reimplemented from NLPInterfacePack::NLPSerialPreprocessExplJac.
Definition at line 127 of file NLPInterfacePack_ExampleNLPBanded.cpp.

bool NLPInterfacePack::ExampleNLPBanded::is_initialized ( ) const [virtual]

Reimplemented from NLPInterfacePack::NLPSerialPreprocessExplJac.
Definition at line 138 of file NLPInterfacePack_ExampleNLPBanded.cpp.

value_type NLPInterfacePack::ExampleNLPBanded::max_var_bounds_viol ( ) const [virtual]

Implements NLPInterfacePack::NLP.
Definition at line 143 of file NLPInterfacePack_ExampleNLPBanded.cpp.

bool NLPInterfacePack::ExampleNLPBanded::nlp_selects_basis ( ) const [virtual]

Reimplemented from NLPInterfacePack::NLPSerialPreprocess.
Definition at line 363 of file NLPInterfacePack_ExampleNLPBanded.cpp.

bool NLPInterfacePack::ExampleNLPBanded::imp_nlp_has_changed ( ) const [protected, virtual]

Reimplemented from NLPInterfacePack::NLPSerialPreprocess.
Definition at line 150 of file NLPInterfacePack_ExampleNLPBanded.cpp.

size_type NLPInterfacePack::ExampleNLPBanded::imp_n_orig ( ) const [protected, virtual]

Implements NLPInterfacePack::NLPSerialPreprocess.
Definition at line 155 of file NLPInterfacePack_ExampleNLPBanded.cpp.

size_type NLPInterfacePack::ExampleNLPBanded::imp_m_orig ( ) const [protected, virtual]

Implements NLPInterfacePack::NLPSerialPreprocess.
Definition at line 160 of file NLPInterfacePack_ExampleNLPBanded.cpp.

size_type NLPInterfacePack::ExampleNLPBanded::imp_mI_orig ( ) const [protected, virtual]

Implements NLPInterfacePack::NLPSerialPreprocess.
Definition at line 166 of file NLPInterfacePack_ExampleNLPBanded.cpp.

const DVectorSlice NLPInterfacePack::ExampleNLPBanded::imp_xinit_orig ( ) const [protected, virtual]

Implements NLPInterfacePack::NLPSerialPreprocess.
Definition at line 172 of file NLPInterfacePack_ExampleNLPBanded.cpp.

bool NLPInterfacePack::ExampleNLPBanded::imp_has_var_bounds ( ) const [protected, virtual]

Implements NLPInterfacePack::NLPSerialPreprocess.
Definition at line 177 of file NLPInterfacePack_ExampleNLPBanded.cpp.

const DVectorSlice NLPInterfacePack::ExampleNLPBanded::imp_xl_orig ( ) const [protected, virtual]

Implements NLPInterfacePack::NLPSerialPreprocess.
Definition at line 182 of file NLPInterfacePack_ExampleNLPBanded.cpp.

const DVectorSlice NLPInterfacePack::ExampleNLPBanded::imp_xu_orig ( ) const [protected, virtual]

Implements NLPInterfacePack::NLPSerialPreprocess.
Definition at line 187 of file NLPInterfacePack_ExampleNLPBanded.cpp.

const DVectorSlice NLPInterfacePack::ExampleNLPBanded::imp_hl_orig ( ) const [protected, virtual]

Implements NLPInterfacePack::NLPSerialPreprocess.
Definition at line 192 of file NLPInterfacePack_ExampleNLPBanded.cpp.

const DVectorSlice NLPInterfacePack::ExampleNLPBanded::imp_hu_orig ( ) const [protected, virtual]

Implements NLPInterfacePack::NLPSerialPreprocess.
Definition at line 197 of file NLPInterfacePack_ExampleNLPBanded.cpp.

void NLPInterfacePack::ExampleNLPBanded::imp_calc_f_orig ( const DVectorSlice & x_full,

bool newx,

const ZeroOrderInfoSerial & zero_order_info

) const [protected, virtual]

Implements NLPInterfacePack::NLPSerialPreprocess.
Definition at line 202 of file NLPInterfacePack_ExampleNLPBanded.cpp.

void NLPInterfacePack::ExampleNLPBanded::imp_calc_c_orig ( const DVectorSlice & x_full,

bool newx,

const ZeroOrderInfoSerial & zero_order_info

) const [protected, virtual]

Implements NLPInterfacePack::NLPSerialPreprocess.
Definition at line 213 of file NLPInterfacePack_ExampleNLPBanded.cpp.

void NLPInterfacePack::ExampleNLPBanded::imp_calc_h_orig ( const DVectorSlice & x_full,

bool newx,

const ZeroOrderInfoSerial & zero_order_info

) const [protected, virtual]

Implements NLPInterfacePack::NLPSerialPreprocess.
Definition at line 258 of file NLPInterfacePack_ExampleNLPBanded.cpp.

void NLPInterfacePack::ExampleNLPBanded::imp_calc_Gf_orig ( const DVectorSlice & x_full,

bool newx,

const ObjGradInfoSerial & obj_grad_info

) const [protected, virtual]

Implements NLPInterfacePack::NLPSerialPreprocess.
Definition at line 282 of file NLPInterfacePack_ExampleNLPBanded.cpp.

bool NLPInterfacePack::ExampleNLPBanded::imp_get_next_basis ( IVector * var_perm_full,

IVector * equ_perm_full,

size_type * rank_full,

size_type * rank

) [protected, virtual]

Reimplemented from NLPInterfacePack::NLPSerialPreprocess.
Definition at line 293 of file NLPInterfacePack_ExampleNLPBanded.cpp.

void NLPInterfacePack::ExampleNLPBanded::imp_report_orig_final_solution ( const DVectorSlice & x_orig,

const DVectorSlice * lambda_orig,

const DVectorSlice * lambdaI_orig,

const DVectorSlice * nu_orig,

bool is_optimal

) const [protected]

Definition at line 352 of file NLPInterfacePack_ExampleNLPBanded.cpp.

size_type NLPInterfacePack::ExampleNLPBanded::imp_Gc_nz_orig ( ) const [protected, virtual]

Implements NLPInterfacePack::NLPSerialPreprocessExplJac.
Definition at line 370 of file NLPInterfacePack_ExampleNLPBanded.cpp.

size_type NLPInterfacePack::ExampleNLPBanded::imp_Gh_nz_orig ( ) const [protected, virtual]

Implements NLPInterfacePack::NLPSerialPreprocessExplJac.
Definition at line 375 of file NLPInterfacePack_ExampleNLPBanded.cpp.

void NLPInterfacePack::ExampleNLPBanded::imp_calc_Gc_orig ( const DVectorSlice & x_full,

bool newx,

const FirstOrderExplInfo & first_order_expl_info

) const [protected, virtual]

Implements NLPInterfacePack::NLPSerialPreprocessExplJac.
Definition at line 380 of file NLPInterfacePack_ExampleNLPBanded.cpp.

void NLPInterfacePack::ExampleNLPBanded::imp_calc_Gh_orig ( const DVectorSlice & x_full,

bool newx,

const FirstOrderExplInfo & first_order_expl_info

) const [protected, virtual]

Implements NLPInterfacePack::NLPSerialPreprocessExplJac.
Definition at line 459 of file NLPInterfacePack_ExampleNLPBanded.cpp.

The documentation for this class was generated from the following files:

Generated on Thu Sep 18 12:36:39 2008 for MOOCHO by

1.3.9.1

NLPInterfacePack::ExampleNLPBanded Class Reference

Constructors / initializers

Overridden public members from NLP

Overridden from NLPVarReductPerm

Overridden protected methods from NLPSerialPreprocess

Overridden protected methods from NLPSerialPreprocessExplJac

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation