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XPRSrepairinfeas

Purpose
Provides a simplified interface for XPRSrepairweightedinfeas.
Topic area
Infeasibility
Synopsis
int XPRS_CC XPRSrepairinfeas (XPRSprob prob, int *p_status, char penalty, char phase2, char flags, double lepref, double gepref, double lbpref, double ubpref, double delta);
Arguments
prob 
The current problem.
p_status 
The status after the relaxation:
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.
penalty 
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.
phase2 
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.
flags 
Specifies flags to be passed to XPRSoptimize.
lepref 
Preference for relaxing the less or equal side of row.
gepref 
Preference for relaxing the greater or equal side of a row.
lbpref 
Preferences for relaxing lower bounds.
ubpref 
Preferences for relaxing upper bounds.
delta 
The relaxation multiplier in the second phase -1. For console use -d value. 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.
Related controls
Integer
DEFAULTALG 
Forced algorithm selection (default for repairinfeas is primal).

Further information
1. This function currently does not apply to general nonlinear problems.
2. 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.
3. A preference of 0 results in the row or bound not being relaxed.
4. A negative preference indicates that a quadratic penalty cost should be applied. This can specified on a per constraint side or bound basis.
5. Note that the set of preferences are scaling independent.
6. 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.
7. Note that on some problems, slight modifications of delta may affect the value of the original objective drastically.
8. The default value for delta in the console is 0.001.
9. Note that because of their special associated modeling properties, binary and semi-continuous variables are not relaxed.
10. 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.
11. If penalty 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
lepref = rows aTx - aux_var = b 1/lepref*aux_var 1/lepref*aux_var2
lepref <= rows aTx - aux_var <= b 1/lepref*aux_var 1/lepref*aux_var2
gepref = rows aTx + aux_var = b 1/gepref*aux_var 1/gepref*aux_var2
gepref >= rows aTx + aux_var >= b 1/gepref*aux_var 1/gepref*aux_var2
ubpref upper bounds xi - aux_var <= u 1/ubpref*aux_var 1/ubpref*aux_var2
lbpref lower bounds xi + aux_var >= l 1/lbpref*aux_var 1/lbpref*aux_var2


12. If an irreducible infeasible set (IIS) has been identified, the generated IIS(s) are accessible through the IIS retrieval functions, see NUMIIS and XPRSgetiisdata.
Related topics
XPRSrepairweightedinfeas, XPRSoptimize, The Infeasibility Repair Utility.

Parent Topic Console and Library Functions

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