abstract interface for PSCModel for the model selection routine select_model() More...
#include <PSCModelParametersObject.hxx>
Public Member Functions | |
| int | init (const BundleParameters &bp) |
| initialize BundleParameters to given values, if bp is a SumModleParametersObject alos set n_local_models to its values, otherwise leave it unchanged | |
| PSCModelParametersObject (const CBout *cb=0, int cbinc=-1) | |
| default constructor | |
| PSCModelParametersObject (const BundleParameters &bp, const CBout *cb=0, int cbinc=-1) | |
| copy constructor for BundleParameters | |
| PSCModelParametersObject (const PSCModelParametersObject &sms) | |
| copy constructor | |
| virtual | ~PSCModelParametersObject () |
| virtual destructor, implemented in PSCModelParameters.cxx | |
| int | get_minorant (MinorantPointer &mp, CH_Matrix_Classes::Real &mp_coeff, const CH_Matrix_Classes::Matrix &P, const CH_Matrix_Classes::Matrix &d, PSCOracle *oracle, CH_Matrix_Classes::Integer modification_id) |
| Compute the aggregate minornat corresponding to the matrix P*Diag(d)*P'/sum(d) for the given oracle and aggregate it to (or, if empty or mp_coeff=0., store it in) mp; P has orthonormal columns and d is a nonengative vector of appropriate size. | |
| virtual int | select_model (CH_Matrix_Classes::Matrix &modelvecs, MinorantPointer &model_aggregate, CH_Matrix_Classes::Matrix &topvecs, CH_Matrix_Classes::Matrix &Ritz_values, CH_Matrix_Classes::Integer &activedim, CH_Matrix_Classes::Integer &keepsize, CH_Matrix_Classes::Integer &skippedsize, CH_Matrix_Classes::Real primal_Ritzval, const CH_Matrix_Classes::Matrix &primaleigs, const CH_Matrix_Classes::Matrix &primalvecs, const MinorantPointer &primal_aggregate, CH_Matrix_Classes::Real primal_aggregate_coeff, CH_Matrix_Classes::Real growthrate, const CH_Matrix_Classes::Matrix &primalgrowth, const CH_Matrix_Classes::Matrix &dualgrowth, const CH_Matrix_Classes::Matrix &cand_Ritzvec, const CH_Matrix_Classes::Matrix &cand_Ritzval, PSCOracle *oracle, CH_Matrix_Classes::Integer modification_id, FunctionTask function_task, CH_Matrix_Classes::Real function_factor, BundleModel::ModelUpdate model_update, CH_Matrix_Classes::Integer center_id, const CH_Matrix_Classes::Matrix ¢er_y, CH_Matrix_Classes::Integer cand_id, const CH_Matrix_Classes::Matrix &cand_y, CH_Matrix_Classes::Real model_maxviol, CH_Matrix_Classes::Real diffval_center_aggregate, BundleProxObject &H)=0 |
| PSCModel calls this for selecting the next positive semidefinite model. More... | |
 Public Member Functions inherited from ConicBundle::CBout | |
| virtual void | set_out (std::ostream *out=0, int print_level=1) |
| Specifies the output level (out==NULL: no output at all, out!=NULL and level=0: errors and warnings, level>0 increasingly detailed information) More... | |
| virtual void | set_cbout (const CBout *cb, int incr=-1) |
| Specifies the output level relative to the given CBout class. More... | |
| void | clear_cbout () |
| reset to default settings (out=0,print_level=1) | |
| CBout (const CBout *cb=0, int incr=-1) | |
| calls set_cbout | |
| CBout (std::ostream *outp, int pl=1) | |
| initialize correspondingly | |
| CBout (const CBout &cb, int incr=0) | |
| copy constructor | |
| virtual bool | cb_out (int pl=-1) const |
| Returns true if out!=0 and (pl<print_level), pl<0 should be used for WARNINGS and ERRORS only, pl==0 for usual output. | |
| std::ostream & | get_out () const |
| If cb_out() returned true, this returns the output stream, but it will abort if called with out==0. | |
| std::ostream * | get_out_ptr () const |
| returns the pointer to the output stream | |
| int | get_print_level () const |
| returns the print_level | |
| virtual int | mfile_data (std::ostream &out) const |
| writes problem data to the given outstream | |
| Public Member Functions inherited from ConicBundle::BundleParameters | |
| virtual int | get_max_model_size () const |
| returns the value of the variable | |
| virtual int | get_max_bundle_size () const |
| returns the value of the variable | |
| virtual int | get_update_rule () const |
| returns the value of the variable | |
| virtual int | set_max_model_size (int mms) |
| sets the value of the variable | |
| virtual int | set_max_bundle_size (int mbs) |
| sets the value of the variable | |
| virtual int | set_update_rule (int ur) |
| sets the value of the variable | |
| BundleParameters (const BundleParameters &bp) | |
| often works well: small model of size 2 and some history in bundle size for use in scaling | |
| BundleParameters (int modelsize=-1, int bundlesize=-1, int updaterule=-1) | |
| often works well for fast initial progress: small model of size 2 and some history in bundle size for use in scaling; default values give no preference at all | |
| virtual | ~BundleParameters () |
| virtual destructor | |
| virtual BundleParameters * | clone_BundleParameters () const |
| return a new clone object of this on the heap (caller needs to delete the result) | |
Additional Inherited Members | |
| Protected Attributes inherited from ConicBundle::BundleParameters | |
| int | max_model_size |
| maximum number of minorants to be selected for the cutting model (numbers<=1 for no limit, numbers >=2 impose a strict limit) | |
| int | max_bundle_size |
| suggested maximum number of latest minorants stored for use in a model, for constructing variable metric information etc. (negative numbers give no preference; the size may be increased internally in case of confliciting requirements, eg. in n_model_size or by variable metric routines) | |
| int | update_rule |
| in case several update rules are available | |
Detailed Description
abstract interface for PSCModel for the model selection routine select_model()
Because PSCModel implements a model for an AffineMatrixFunction given support function over the positive semidefinite cone, all subgradients are described by points inside this cone. For generating the model it suffices to know the extreme rays or faces. These may described by an orthonormal basis of the subspace of the eigenspaces of nonzero eigenvales. There is no need to consider the generated minorants at all as long as the generating primal matrices are covered by the subspace.
The model is a face of the semidefinite cone spanned by the orthonormal columns of modelvecs – this face includes the candidate and maybe part of the aggregate – possibly in convex combination with a particular positive semidefinite matrix that is needed to span the aggregate; in slight abuse of notation this additional matrix is called the model_aggregate and its conribution to the full aggregate is the model_aggregate_coeff. The eigenvector-eigenvalue pair primalvecs and primaleigs (sorted nonincreasingly) describe the part of the aggregate in the face spanned by modelvecs on input; the columns of primalvecs are also orthonormal and span the same space as modelvecs on input. growthrate, primalgrowth and dualgrowth help to estimate how many of the eigenvalues could actually be active in the final optimal solution (the interior point code never gets to zero eigenvalues). For good convergence it seems important to keep at least the part that is reduced slower than the dual side and maybe more in addition to the new subspace due to the new eigenvalue computation.
The results of the oracle call in the candidate point cand_y are stored in cand_Ritzvecs and cand_Ritzvals (sorted nonincreasingly). Due to numerical imprecision or early termination they need not deliver the actual maximal eigenvectors and eigenvalues. In order to obtain a more stable guess of those, they are used together with the previously important subspace to first form the common subspace of both and to determine the spectral decomposition of the projection of the AffineMatrixFunction at cand_y. The results for the projected matrix are stored in topvecs (orthonormal columns) and Ritz_values (sorted nondecreasingly). Quite often the maximum Ritz_value is a bit larger than the value returned by the eigenvalue computation and the first column of topvecs is typically a better estimate tan that of cand_Ritzvecs, but the latter brings in more new direction infomation.
The task of this routine is to
- form the new modelvecs basis from this information
- decide how many of the topmost Ritz_values and topvecs should be regarded as active (returned in activedim),
- decide how many of the topmost primaleigs and primalvecs are actually included and return this number in modelvecs (all smaller ones will be aggregated in model_aggregate afterwards outside this routine),
- decide how many additional elements of the topmost Ritz_values and topvecs should be kept on top of activedim for the purpose of using this in variable metric heuristics. The dimension of this additional subspace is returned in skippedsize. The subspace of topvecs (and the corresponding elements of Ritz_values) beyond the first activedim+skippedsize elemnts should be deleted here, so that the matrix does not grow arbitrarily (usually it gets much bigger than hoped for anyways)
Member Function Documentation
◆ select_model()
PSCModel calls this for selecting the next positive semidefinite model.
- Parameters
-
[in,out] modelvecs on input: orthonormal basis of the subspace used in the last semidefinite model on output: orthonormal subspace basis to be used in the next semidefinite model, it includes the subspace of the primalvecs of the keepsize largest primaleigs. In particular for null steps the remaining columns of primalvecs with nonzero primaleigs have to be included with the current aggregate in a new aggregate of the model; this will be taken care of outside this routine aftwards [in,out] model_aggregate (MinorantPointer) aggregate in use in the last and then the next model. [in,out] topvecs on input: orthonormal basis of the collected subspace that is supposed to approximate the eigenspace to the largest eigenvalues, see Ritz_values on output: same thing but maybe reduced in size [in,out] Ritz_values on input: Ritz_values in cand_y for the vectors in topvecs on output: same thing but maybe reduced in size as in topvecs [in,out] activedim on input: the dimension of the subspace (first columns in topvecs) regarded as active in the last iterations of the bundle subproblem solution on output: the dimension of the subspace (first columns of topvecs) regarded as (maybe weakly) active now (typically it will increase during null steps and may be tightened at descent steps) [out] keepsize columns 0..keepsize-1 of primalvecs (corresponding to the keepsize largest primaleigs) are included in modelvecs. The remaining columns need to be aggregated afterwards into the aggregate of the model [out] skippedsize columns activedim..activedim+skippedsize-1 of topvecs should be used for setting up the scaling matrix after descent steps. [in] primal_Ritzval the (common) Ritz value of the active subspace of the model (if not available use some guess like Ritz_values(0)) [in] primaleigs eigenvalues of the last primal semdifinite model matrix (sorted nonincreasingly) [in] primalvecs corresponding (orthonormal) eigenvectors to primaleigs [in] primal_aggregate (MinorantPointer) aggregate in use in the last model. [in] primal_aggregate_coeff coefficient on how strongly the aggregated was used in the last primal solution to the model [in] growthrate (Real) factor <X,Z>/<X^-,Z^->, where X^- and Z⁻- are the last but one iterates of the interior point method [in] primalgrowth (Matrix) factor by which primaleigs changed in the last interior point iteration [in] dualgrowth (Matrix) factor by which the dual Ritz values to primalvecs changed during the last interior point iteration [in] cand_Ritzvec (const Matrix&) the (orthonormal) vectors returned by the evaluation call to the oracle [in] cand_Ritzval (const Matrix&) the Ritz values of cand_Ritzvec returned by the evaluation call to the oracle [in] oracle gives access to the evaluation oracle [in] modification_id the identifier for the current version of the function accounting for dynamic modifications [in] function_task see FunctionTask [in] function_factor interpreted according to function_task and the coefficients sum up to at most this value [in] model_update informs about whether cand_y is the result of a null_step or descent_step or a new set up. [in] center_id the identifier of the center point [in] center_y the center point [in] cand_id the identifier of the candidate point [in] cand_y the candidate (mostly differnt from the center), close to it the model should be good [in] model_maxviol a minorant violated by this would have caused a null step [in] diffval_center_aggregate difference of center value to aggregate value (nonnegative, without function_factor) [in] H the variable metric used in the proximal term (function_factor is already removed in this)
- Returns
- 0 on success
- 1 on failure
Implemented in ConicBundle::PSCModelParameters.
Referenced by PSCModelParametersObject().
The documentation for this class was generated from the following file:
