Initializing help system before first use

XPRSrepairweightedinfeasbounds (REPAIRINFEAS)

Purpose
An extended version of XPRSrepairweightedinfeas that allows for bounding the level of relaxation allowed.
Topic area
Infeasibility
Synopsis
int XPRS_CC XPRSrepairweightedinfeasbounds(XPRSprob prob, int * p_status, const double lepref[], const double gepref[], const double lbpref[], const double ubpref[], const double lerelax[], const double gerelax[], const double lbrelax[], const double ubrelax[], char phase2, double delta, const char *flags);
REPAIRINFEAS -[pflags] -[oflags] -[gflags] -[lrp value] -[grp value] -[lbp value] -[ubp value] -[lrb value] -[grb value] -[lbb value] -[ubb value] -[d value] -[r]
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.
lepref 
Array of size ROWS containing the preferences for relaxing the less or equal side of row. For the console use -lrp value.
gepref 
Array of size ROWS containing the preferences for relaxing the greater or equal side of a row. For the console use -grp value.
lbpref 
Array of size COLS containing the preferences for relaxing lower bounds. For the console use -lbp value.
ubpref 
Array of size COLS containing preferences for relaxing upper bounds. For the console use -ubp value.
lerelax 
Array of size ROWS containing the upper bounds on the amount the less or equal side of a row can be relaxed. For the console use -lrb value.
gerelax 
Array of size ROWS containing the upper bounds on the amount the greater or equal side of a row can be relaxed. For the console use -grb value.
lbrelax 
Array of size COLS containing the upper bounds on the amount the lower bounds can be relaxed. For the console use -lbb value.
ubrelax 
Array of size COLS containing the upper bounds on the amount the upper bounds can be relaxed. For the console use -ubb value.
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.
delta 
The relaxation multiplier in the second phase -1.
flags 
Specifies flags to be passed to XPRSoptimize.
r 
If a summary of the violated variables and constraints should be printed after the relaxed solution is determined.
y 
Call the global solver (console command only).
Related controls
Double
PENALTYVALUE 
The weighted sum of violations if a solution is identified to the relaxed problem.

Example 
READPROB MYPROB.LP
REPAIRINFEAS -a -d 0.002
This example reads in an infeasible problem and identifies a solution which violates the rows and bounds the least. It then fixes the measure of violations to this value multiplied by 1.002 to slightly increase the freedom in the problem and optimizes the relaxed problem using the original objective function.
Further information
1. This function applies to all problem types.
2. The console command REPAIRINFEAS assumes that all preferences are 1 by default. Use the options -lrp, -grp, -lbp or -ubp to change them. The default limit on the maximum allowed relaxation per row or bound in plus infinity.
3. 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.
4. A preference of 0 results in the row or bound not being relaxed. The higher the preference, the more willing the modeller is to relax a given row or bound.
5. A negative preference indicates that a quadratic penalty cost should be applied. This can specified on a per constraint side or bound basis.
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. Given any row j with preferences lrp=lepref[j] and grp=gepref[j], or variable i with bound preferences ubp=ubpref[i] and lbp=lbpref[i], 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


11. Only positive bounds are applied; a zero or negative bound is ignored and the amount of relaxation allowed for the corresponding row or bound is not limited. The effect of a zero bound on a row or bound would be equivalent with not relaxing it, and can be achieved by setting its preference array value to zero instead, or not including it in the preference arrays.
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
XPRSrepairinfeas ( REPAIRINFEAS), XPRSoptimize, The Infeasibility Repair Utility.

Parent Topic Console and Library Functions

© 2001-2025 Fair Isaac Corporation. All rights reserved. This documentation is the property of Fair Isaac Corporation (“FICO”). Receipt or possession of this documentation does not convey rights to disclose, reproduce, make derivative works, use, or allow others to use it except solely for internal evaluation purposes to determine whether to purchase a license to the software described in this documentation, or as otherwise set forth in a written software license agreement between you and FICO (or a FICO affiliate). Use of this documentation and the software described in it must conform strictly to the foregoing permitted uses, and no other use is permitted.