XSLP_AUGMENTATION

Bit 0: Minimum augmentation. Standard augmentation includes delta vectors for all variables involved in nonlinear terms (in non-constant coefficients or as vectors containing non-constant coefficients). Minimum augmentation includes delta vectors only for variables in non-constant coefficients. This produces a smaller linearization, but there is less control on convergence, because convergence control (for example, step bounding) cannot be applied to variables without deltas.

Bit 1: Even handed augmentation. Standard augmentation treats variables which appear in non-constant coefficients in a different way from those which contain non-constant coefficients. Even-handed augmentation treats them all in the same way by replacing each non-constant coefficient C in a vector V by a new coefficient C*V in the "equals" column (which has a fixed activity of 1) and creating delta vectors for all types of variable in the same way.

Bit 2: Penalty error vectors on all non-linear equality constraints. The linearization of a nonlinear equality constraint is inevitably an approximation and so will not generally be feasible except at the point of linearization. Adding penalty error vectors allows the linear approximation to be violated at a cost and so ensures that the linearized constraint is feasible.

Bit 3: Penalty error vectors on all non-linear inequality constraints. The linearization of a nonlinear constraint is inevitably an approximation and so may not be feasible except at the point of linearization. Adding penalty error vectors allows the linear approximation to be violated at a cost and so ensures that the linearized constraint is feasible.

Bit 4: Penalty vectors to exceed step bounds. Although it has rarely been found necessary or desirable in practice, Xpress-SLP allows step bounds to be violated at a cost. This may help with feasibility but it generally slows down or prevents convergence, so it should be used only if found absolutely necessary.

Bit 5: Use arithmetic means to estimate penalty weights. Penalty weights are estimated from the magnitude of the elements in the constraint or interacting rows. Geometric means are normally used, so that a few excessively large or small values do not distort the weights significantly. Arithmetic means will value the coefficients more equally.

Bit 6: Estimate step bounds from values of row coefficients. If step bounds are to be imposed from the start, the best approach is to provide explicit values for the bounds. Alternatively, Xpress-SLP can estimate the values from the range of estimated coefficient sizes in the relevant rows.

Bit 7: Estimate step bounds from absolute values of row coefficients. If step bounds are to be imposed from the start, the best approach is to provide explicit values for the bounds. Alternatively, Xpress-SLP can estimate the values from the largest estimated magnitude of the coefficients in the relevant rows.

Bit 8: Row-based step bounds. Step bounds are normally applied as bounds on the delta variables. Some applications may find that using explicit rows to bound the delta vectors gives better results.

Bit 9: Penalty error vectors on all constraints. If the linear portion of the underlying model may actually be infeasible, then applying penalty vectors to all rows may allow identification of the infeasibility and may also allow a useful solution to be found.

The recommended setting is bits 2 and 3 (penalty vectors on all nonlinear constraints).