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problem.repairinfeas

problem.repairinfeas

Purpose
Provides a simplified interface for problem.repairweightedinfeas. The returned value is as follows:
  • 0: relaxed optimum found;
  • 1: relaxed problem is infeasible;
  • 2: relaxed problem is unbounded;
  • 3: solution of the relaxed problem regarding the original objective is nonoptimal;
  • 4: error (when return code is nonzero);
  • 5: numerical instability;
  • 6: analysis of an infeasible relaxation was performed, but the relaxation is feasible.

Synopsis
status_code = problem.repairinfeas(pflags, oflags, gflags, lrp, grp, lbp, ubp, delta)
Arguments
pflags 
The type of penalties created from the preferences:
c 
each penalty is the reciprocal of the preference (default);
s 
the penalties are placed in the scaled problem.
oflags 
Controls the second phase of optimization:
o 
use the objective sense of the original problem (default);
x 
maximize the relaxed problem using the original objective;
f 
skip optimization regarding the original objective;
n 
minimize the relaxed problem using the original objective;
i 
if the relaxation is infeasible, generate an irreducible infeasible subset for the analys of the problem;
a 
if the relaxation is infeasible, generate all irreducible infeasible subsets for the analys of the problem.
gflags 
Specifies if the global search should be done:
g 
do the global search (default);
l 
solve as a linear model ignoring the discreteness of variables.
lrp 
Preference for relaxing the less or equal side of row.
grp 
Preference for relaxing the greater or equal side of a row.
lbp 
Preferences for relaxing lower bounds.
ubp 
Preferences for relaxing upper bounds.
delta 
The relaxation multiplier in the second phase -1. A positive value means a relative relaxation by multiplying the first phase objective with ( delta-1), while a negative value means an absolute relaxation, by adding abs(delta) to the first phase objective.
Further information
1. A row or bound is relaxed by introducing a new nonnegative variable that will contain the infeasibility of the row or bound. Suppose for example that row a Tx = b is relaxed from below. Then a new variable (infeasibility breaker) s>=0 is added to the row, which becomes a Tx +s = b. Observe that a Tx may now take smaller values than b. To minimize such violations, the weighted sum of these new variables is minimized.
2. A preference of 0 results in the row or bound not being relaxed.
3. A negative preference indicates that a quadratic penalty cost should be applied. This can specified on a per constraint side or bound basis.
4. Note that the set of preferences are scaling independent.
5. If a feasible solution is identified for the relaxed problem, with a sum of violations p, then the sum of violations is restricted to be no greater than ( 1+delta) p, and the problem is optimized with respect to the original objective function. A nonzero delta increases the freedom of the original problem.
6. Note that on some problems, slight modifications of delta may affect the value of the original objective drastically.
7. Note that because of their special associated modeling properties, binary and semi-continuous variables are not relaxed.
8. The default algorithm for the first phase is the simplex algorithm, since the primal problem can be efficiently warm started in case of the extended problem. These may be altered by setting the value of control DEFAULTALG.
9. If pflags is set such that each penalty is the reciprocal of the preference, the following rules are applied while introducing the auxiliary variables:

Preference    Affects                  Relaxation Cost if pref.>0 Cost if pref.<0
lrp = rows aTx - aux_var = b 1/lrp*aux_var 1/lrp*aux_var2
lrp <= rows aTx - aux_var <= b 1/lrp*aux_var 1/lrp*aux_var2
grp = rows aTx + aux_var = b 1/grp*aux_var 1/grp*aux_var2
grp >= rows aTx + aux_var >= b 1/grp*aux_var 1/grp*aux_var2
ubp upper bounds xi - aux_var <= u 1/ubp*aux_var 1/ubp*aux_var2
lbp lower bounds xi + aux_var >= l 1/lbp*aux_var 1/lbp*aux_var2


10. If an irreducible infeasible set (IIS) has been identified, the generated IIS(s) are accesible through the IIS retrieval functions, see NUMIIS and problem.getiisdata.
Related topics
problem.repairweightedinfeas.

Parent Topic Reference Manual