Clp
1.17.6

Attempt to fix variables by bounding reduced costs. More...
#include <CoinPresolveDual.hpp>
Classes  
struct  action 
Postsolve (bound restore) instruction. More...  
Public Member Functions  
~remove_dual_action ()  
Destructor. More...  
const char *  name () const 
Name. More...  
void  postsolve (CoinPostsolveMatrix *prob) const 
Postsolve. More...  
Public Member Functions inherited from CoinPresolveAction  
CoinPresolveAction (const CoinPresolveAction *next)  
Construct a postsolve object and add it to the transformation list. More...  
void  setNext (const CoinPresolveAction *nextAction) 
modify next (when building rather than passing) More...  
virtual  ~CoinPresolveAction () 
Virtual destructor. More...  
Static Public Member Functions  
static const CoinPresolveAction *  presolve (CoinPresolveMatrix *prob, const CoinPresolveAction *next) 
Attempt to fix variables by bounding reduced costs. More...  
Static Public Member Functions inherited from CoinPresolveAction  
static void  throwCoinError (const char *error, const char *ps_routine) 
Stub routine to throw exceptions. More...  
Private Member Functions  
remove_dual_action (int nactions, const action *actions, const CoinPresolveAction *next)  
Constructor with postsolve actions. More...  
Private Attributes  
const int  nactions_ 
Count of bound restore entries. More...  
const action *  actions_ 
Bound restore entries. More...  
Additional Inherited Members  
Public Attributes inherited from CoinPresolveAction  
const CoinPresolveAction *  next 
The next presolve transformation. More...  
Attempt to fix variables by bounding reduced costs.
The reduced cost of x_j is d_j = c_j  y*a_j (1). Assume minimization, so that at optimality d_j >= 0 for x_j nonbasic at lower bound, and d_j <= 0 for x_j nonbasic at upper bound.
For a slack variable s_i, c_(n+i) = 0 and a_(n+i) is a unit vector, hence d_(n+i) = y_i. If s_i has a finite lower bound and no upper bound, we must have y_i <= 0 at optimality. Similarly, if s_i has no lower bound and a finite upper bound, we must have y_i >= 0.
For a singleton variable x_j, d_j = c_j  y_i*a_ij. Given x_j with a single finite bound, we can bound d_j greater or less than 0 at optimality, and that allows us to calculate an upper or lower bound on y_i (depending on the bound on d_j and the sign of a_ij).
Now we have bounds on some subset of the y_i, and we can use these to calculate upper and lower bounds on the d_j, using bound propagation on (1). If we can manage to bound some d_j as strictly positive or strictly negative, then at optimality the corresponding variable must be nonbasic at its lower or upper bound, respectively. If the required bound is lacking, the problem is unbounded.
Definition at line 35 of file CoinPresolveDual.hpp.
remove_dual_action::~remove_dual_action  (  ) 
Destructor.

inlineprivate 
Constructor with postsolve actions.
Definition at line 68 of file CoinPresolveDual.hpp.

inlinevirtual 

static 
Attempt to fix variables by bounding reduced costs.
Always scans all variables. Propagates bounds on reduced costs until there's no change or until some set of variables can be fixed.

virtual 
Postsolve.
In addition to fixing variables (handled by make_fixed_action), we may need use our own postsolve to restore constraint bounds.
Implements CoinPresolveAction.

private 
Count of bound restore entries.
Definition at line 77 of file CoinPresolveDual.hpp.

private 
Bound restore entries.
Definition at line 79 of file CoinPresolveDual.hpp.