ConicBundle

Oracle interface for minimization of the maximum eigenvalue of an affine matrix function or, equivalently, Lagrangian relaxation of semidefinite programs. More...
#include <PSCOracle.hxx>
Public Member Functions  
virtual Minorant *  generate_minorant (const CH_Matrix_Classes::Matrix &P)=0 
generates the minorant that arises from the gram matrix PP^T (maybe including some primal information for primal aggregation). More...  
virtual int  svec_projection (CH_Matrix_Classes::Matrix &svec_offset, CH_Matrix_Classes::Matrix &svec_coeffs, const CH_Matrix_Classes::Matrix &P, const CH_Matrix_Classes::Indexmatrix *index_subset=0)=0 
compute svec representation of the projected coefficient matrices More...  
virtual int  evaluate (const CH_Matrix_Classes::Matrix ¤t_point, const CH_Matrix_Classes::Matrix &bundlevecs, const double relprec, const double Ritz_bound, CH_Matrix_Classes::Matrix &Ritz_vectors, CH_Matrix_Classes::Matrix &Ritz_values, PSCPrimalExtender *&primal_extender)=0 
virtual int  evaluate_projection (const CH_Matrix_Classes::Matrix ¤t_point, const CH_Matrix_Classes::Matrix &P, const double relprec, CH_Matrix_Classes::Matrix &projected_Ritz_vectors, CH_Matrix_Classes::Matrix &projected_Ritz_values)=0 
virtual int  left_right_product (int i, const CH_Matrix_Classes::Matrix &P, const CH_Matrix_Classes::Matrix &Q, CH_Matrix_Classes::Matrix &G)=0 
virtual int  apply_modification (const OracleModification &, const CH_Matrix_Classes::Matrix *, const CH_Matrix_Classes::Matrix *, bool &, bool &, bool &, MinorantExtender *&) 
This routine need not be implemented unless variables (constraints in Lagrangean relaxation) are added or deleted on the fly. More...  
virtual bool  check_correctness () const 
switch on/off some correctnes checks on the oracle  
Public Member Functions inherited from ConicBundle::ModifiableOracleObject  
virtual  ~ModifiableOracleObject () 
virtual destructor  
Oracle interface for minimization of the maximum eigenvalue of an affine matrix function or, equivalently, Lagrangian relaxation of semidefinite programs.
Within the setting explained in abstract positive semidefinite cone oracle the abstract class PSCOracle defines a matrix free interface to maximum eigenvalue/eigenvector and the action of the affine matrix function for the spectral bundle cutting model implemented in PSCModel. In particular, it provides in
For a concrete implementation of PSCOracle see ConicBundle::AffineMatrixFunction .

inlinevirtual 
This routine need not be implemented unless variables (constraints in Lagrangean relaxation) are added or deleted on the fly.
The routine is only called by the solver if the variables indeed get modified by the solver or a modification is passed on by the user via the solver interface. oracle_modification is then used to either transfer user supplied instructions to the oracle on how to modify itself or to inform the oracle about changes the solver was asked to perform on the variables. If available, the solver will also show the effect of these changes on the center point in new_center and old_center; if these are not available then they hold NULL. A user supplied oracle_modification will be checked for consistency with the actual changes in the variables and mismatches will cause failures.
The remaining variables are output variables by which the oracle tells the solver which information has a chance to be preserved in view of these changes. If e.g. the deletion of some nonzero variables invalidates the function value in the new center, the oracle has to set discard_objective_in_center=true. If the entire model cannot be preserved (this includes the aggregates and the function values), the oracle needs to set discard_model=true; If only aggregate minorants cannot be preserved, the oracle needs to set discard_aggregates=true; in the current implementation of PSCModel this removes all minorants generated by generate_minorant() because each of them is typically generated by more than one Ritz vector. Whenever new variables were added, the model can only be preserved if the remaining minorants (maybe without aggregates) can be extended for these new variables. In this case the oracle has to supply the appropriate MinorantExtender via minorant_extender and only those minorants will be kept for which this operation succeeds.
Return value 0 indicates that these actions allow to continue without errors, other return values result in an overall error on these changes.
Reimplemented from ConicBundle::ModifiableOracleObject.
Reimplemented in ConicBundle::PSCAffineFunction.

pure virtual 
compute maximum eigenvalue of the matrix C+opAt(y)
current_point  argument = current variables = position where to evaluate the function 
bundlevecs  The columns of the matrix are orthonormal bundle vectors and may help to construct good startig vectors for the eigenvalue computation by iterative methods but have no other use. bundlevecs may have dimension 0. 
relprec  relative precision requirement for objective values leading to descent steps 
Ritz_bound  gives the threshold for a null step; a vector is good enough to yield sufficient improvement if its Ritz value exceeds this Ritz_bound. Otherwise the largest of the returned Ritz_values must be guaranteed to lie within relprec*(max(abs(Ritz_bound),1.)) of the maximum eigenvalue 
Ritz_vectors  on input: if not zero dimensional, the columns of the matrix contains the orthonormal family of Ritz_vectors returned in the previous call; these may help to construct good starting vectors for the eigenvalue computation by iterative methods. 
on output: the columns of the matrix form an orthonormal family that has to contain at least one vector with the following property: is an eigenvector to the maximum eigenvalue or it has a Ritz value that exceeds the null step bound Ritz_bound.
Ritz_values  Ritz_values corresponding to the Ritz_vectors  
primal_extender  
[out]  primal_extender  (PrimalExtender*&) if primal_data or Ritz_vectors provided in minonrants of previous calls now have to be updated due to changes in the primal problem – e.g., this may happen in column generation – one may return a pointer to a PSCPrimalExtender object on the heap. This object will be used by ConicBundle to update all its internally stored Ritz_vectors and primal_data objects in its minorants by calling PrimalExtender::extend on each of these. Afterwards ConicBundle deletes primal_extender. If this is not needed, set the variable to NULL. 
Implemented in ConicBundle::PSCAffineFunction.

pure virtual 
compute maximum eigenvalue of P^T(CopAt(y))P
current_point  argument = current variable values = position where to evaluate the function 
P  orthogonal matrix defining the projection; 
relprec  relative precision requirement 
projected_Ritz_vectors  output: orthognal matrix that contains at least one column vector that is an eigenvector to the maximum eigenvalue of the projected Matrix 
projected_Ritz_values  output: Ritz_values corresponding to the Ritz_vectors 
Implemented in ConicBundle::PSCAffineFunction.

pure virtual 
generates the minorant that arises from the gram matrix PP^T (maybe including some primal information for primal aggregation).
The returned minorant must satisfy offset_gives_value_at_origin()==true. The minorant is passed over to the caller and will be deleted there.
Implemented in ConicBundle::PSCAffineFunction.

pure virtual 
fills row i with vec(P^T*(A_i)*Q)^T (needed for the bundle update and the scaling heuristic in PSCModel)
i  index of the coefficient matrix 
P  left multiplication matrix 
Q  right multiplication matrix 
G  the result is stored in this matrix. 
Implemented in ConicBundle::PSCAffineFunction.

pure virtual 
compute svec representation of the projected coefficient matrices
This always includes the constant cofficient matrix, svec_offset=svec(P^T*C*P). If index_subset==0, row i of svec_coeffs is filled with svec(P^T*A_i*P)^T for i=1,dots,m If index_subset!=0, row i of svec_coeffs holds this for A_{(*index_subset)(i)}
Implemented in ConicBundle::PSCAffineFunction.