Handling Infeasibilities

By default, Xpress-SLP will include penalty error vectors in the augmented SLP structure. This feature adds explicit positive and negative slack vectors to all constraints (or, optionally, just to equality constraints) which include nonlinear coefficients. In many cases, this is itself enough to retain feasibility. There is also an opportunity to add penalty error vectors to all constraints, but this is not normally required.

During cascading (see next section), Xpress-SLP will ensure that the value of a cascaded variable is never set outside its lower and upper bounds (if these have been specified).

Infeasibility Analysis in the Xpress Optimizer

Managing Infeasibility with Xpress KNITRO

XKTR_PARAM_FEASTOL

This is the relative feasibility tolerance applied to a problem.

XKTR_PARAM_FEASTOLABS

This is the corresponding absolute feasibility tolerance.

XKTR_PARAM_INFEASTOL

This is the tolerance for declaring a problem infeasible.

Managing Infeasibility with Xpress-SLP

1. Infeasibility introduced by the error of the approximation, most noticeable when significant steps are made in the linearization.
2. Infeasibility introduced by the activation of penalty breakers, where it was not otherwise possible to make a meaningful step in the linearization.

XSLP_ECFTOL_A

The absolute linearization feasibility tolerance is compared for each constraint in the original, nonlinear problem to its violation by the current solution.

XSLP_ECFTOL_R

The relative linearization feasibility tolerance is compared for each constraint in the original, nonlinear problem to its violation by the current solution, relative to the maximum absolute value of the positive and negative contributions to the constraint.

Penalty Infeasibility Breakers in XSLP