Penalty Infeasibility Breakers in XSLP

XSLP_CURRENTERRORCOST. The control XSLP_ERRORCOST determines the initial value for this cost, while the XSLP_ERRORCOSTFACTOR controls the factor by which it increases if active error vectors remain. The maximum value of the penalty is determined by the control XSLP_ERRORMAXCOST. If the maximum error cost is reached, it is unlikely that XSLP will converge. It is possible in this situation to terminate the solve, by setting bit 11 of XSLP_ALGORITHM. Some problems may be sensitive to the initial value of XSLP_ERRORCOST. If this value is too small relative to the original objective in the model, feasibility will not be sufficiently strongly encouraged during the solution process. This can cause SLP to explore highly infeasible solutions in the early stages, since the original objective will dominate any consideration of feasibility. It is even possible in this case for unboundedness of the linearizations to occur, although SLP is capable of automatic recovery from such a situation. When the initial penalty cost is too high, the penalty term will dominate the objective. This in turn will may lead to initially low quality solutions being explored, with the attendant possibility of numerical errors accumulating. The control XSLP_OBJTOPENALTYCOST guides the process which selects an automatic value for XSLP_ERRORCOST, but determining such a value analytically can be difficult. For some difficult problems, there may be significant benefits to selecting the value directly. Often for infeasible problems, the contribution of the individual constraints to the overall infeasibility is non-uniform. XSLP can automatically associate a weight with each row based upon the magnitude of the terms in the constraint. It is both possible to refine these weights, or alternatively to allow XSLP update them dynamically. The latter case is called escalation, and is controlled by bit 8 of XSLP_ALGORITHM. Devising appropriate weights manually can be difficult, and in most cases it is preferable to leave the identification of these values to Xpress-SLP. However if it is necessary to do, the output of XSLP may provide hints as to appropriate values if detailed logging is enabled. This can be turned on with XSLP_LOG. The most important points in such output are the active error vectors at each iteration, where the most attractive constraints to modify are those which occur regularly in the log in association with non-zero error vectors.