XSLP_AUGMENTATION, SLPAUGMENTATION

Bit map describing the SLP augmentation method(s) to be used

Integer

Bit	Meaning
0	Minimum augmentation.
1	Even handed augmentation.
2	Penalty error vectors on all non-linear equality constraints.
3	Penalty error vectors on all non-linear inequality constraints.
4	Penalty vectors to exceed step bounds.
5	Use arithmetic means to estimate penalty weights.
6	Estimate step bounds from values of row coefficients.
7	Estimate step bounds from absolute values of row coefficients.
8	Row-based step bounds.
9	Penalty error vectors on all constraints.
10	Intial values do not imply an SLP variable.
12	Avoid running an LP around fixed initial values trying to get feasible.

12 (sets bits 2 and 3)

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.

Bit 10: Having an initial value will not cause the augmentation to include the corresponding delta variable; i.e. treat the variable as an SLP variable. Useful to provide initial values necessary in the first linearization in case of a minimal augmentation, or as a convenience option when it's easiest to set an initial value for all variables for some reason.

Bit 12: Unless this bit is set, if almost all variables have initial values, an LP can be solved with all variables with initial values fixed to those, to try to extend the partial initial solution to a feasible solution.

The following constants are provided for setting these bits:

Setting bit 0	XSLP_MINIMUMAUGMENTATION
Setting bit 1	XSLP_EVENHANDEDAUGMENTATION
Setting bit 2	XSLP_EQUALITYERRORVECTORS
Setting bit 3	XSLP_ALLERRORVECTORS
Setting bit 4	XSLP_PENALTYDELTAVECTORS
Setting bit 5	XSLP_AMEANWEIGHT
Setting bit 6	XSLP_SBFROMVALUES
Setting bit 7	XSLP_SBFROMABSVALUES
Setting bit 8	XSLP_STEPBOUNDROWS
Setting bit 9	XSLP_ALLROWERRORVECTORS
Setting bit 10	XSLP_NOUPDATEIFONLYIV
Setting bit 12	XSLP_SKIPIVLPHEURISTICS

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

XSLPconstruct