XPRSrepairweightedinfeas

Purpose

By relaxing a set of selected constraints and bounds of an infeasible problem, it attempts to identify a 'solution' that violates the selected set of constraints and bounds minimally, while satisfying all other constraints and bounds. Among such solution candidates, it selects one that is optimal regarding the original objective function. For the console version, see REPAIRINFEAS.

Synopsis

 int XPRS_CC XPRSrepairweightedinfeas(XPRSprob prob, int * p_status, const double lepref[], const double gepref[], const double lbpref[], const double ubpref[], char phase2, double delta, const char *flags);

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.

gepref

Array of size ROWS containing the preferences for relaxing the greater or equal side of a row.

lbpref

Array of size COLS containing the preferences for relaxing lower bounds.

ubpref

Array of size COLS containing preferences for relaxing upper bounds.

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.

Related controls

Double

PENALTYVALUE

The weighted sum of violations if a solution is identified to the relaxed problem.

Example

See also example repair.c.

Further information

1. This function applies to all problem types.

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. The higher the preference, the more willing the modeller is to relax a given row or bound.

4. The weight of each infeasibility breaker in the objective minimizing the violations is 1/p, where p is the preference associated with the infeasibility breaker. Thus the higher the preference is, the lower a penalty is associated with the infeasibility breaker while minimizing the violations.

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. The default value for delta in the console is 0.001.

8. Note that because of their special associated modeling properties, binary and semi-continuous variables are not relaxed.

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:


Pref. array	Affects	Relaxation	Cost if pref.>0	Cost if pref.<0
lepref	= rows	a^Tx - aux_var = b	1/lrp*aux_var	1/lrp*aux_var²
lepref	<= rows	a^Tx - aux_var <= b	1/lrp*aux_var	1/lrp*aux_var²
gepref	= rows	a^Tx + aux_var = b	1/grp*aux_var	1/grp*aux_var²
gepref	>= rows	a^Tx + aux_var >= b	1/grp*aux_var	1/grp*aux_var²
ubpref	upper bounds	x_i - aux_var <= u	1/ubp*aux_var	1/ubp*aux_var²
lbpref	lower bounds	x_i + 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 accessible through the IIS retrieval functions, see NUMIIS and XPRSgetiisdata.

Contents

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XPRSrepairweightedinfeas