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XPRSaddpwlcons, XPRSaddpwlcons64

XPRSaddpwlcons, XPRSaddpwlcons64

Purpose
Adds one or more piecewise linear constraints to the problem. Each piecewise linear constraint y = f(x) consists of an (input) column x, a (different) resultant (output column) y and a piecewise linear function f. The piecewise linear function f is described by at least two breakpoints, which are given as combinations of x- and y-values. Discontinuous piecewise linear functions are supported, in this case both the left and right limit at a given point need to be entered as breakpoints. To differentiate between left and right limit, the breakpoints need to be given as a list with non-decreasing x-values.
Synopsis
int XPRS_CC XPRSaddpwlcons(XPRSprob prob, int npwls, int npoints, const int col[], const int resultant[], const int start[], const double xval[], const double yval[]);

int XPRS_CC XPRSaddpwlcons64(XPRSprob prob, int npwls, XPRSint64 npoints, const int col[], const int resultant[], const XPRSint64 start[], const double xval[], const double yval[]);
Arguments
prob 
The current problem.
npwls 
The number of piecewise linear constraints to add.
npoints 
The total number of breakpoints of all piecewise linear constraints that should be added.
col 
Integer array of length npwls containing the indices of the input variables x of the piecewise linear functions.
resultant 
Integer array of length npwls containing the indices of the output variables y of the piecewise linear functions.
start 
Integer array of length npwls containing the start index of each piecewise linear constraint in the xval and yval arrays.
xval 
Double array of length npoints containing the x-values of the breakpoints.
yval 
Double array of length npoints containing the y-values of the breakpoints.
Related controls
Integer
PWLDUALREDUCTIONS 
Controls whether dual reductions may be applied to reduce the number of added variables and constraints.

Example
The following example adds a new piecewise linear constraint y = f(x), where

f(x) = -x if x < 0
f(x) = 1 if 0 <= x <= 2
f(x) = 2x-3 if x > 2

This function can be defined using the breakpoints (x = -1, y = 1), (0,0), (0,1), (2,1), (3,3) (note that the first breakpoint could also be replaced, e.g., by (x = -2, y = 2), similarly for the last): 
int col[] = {0};
int resultant[] = {1};
int start[] = {0};
double xval[] = {-1,0,0,2,3};
double yval[] = {1,0,1,1,3};
...
XPRSaddpwlcons(prob,1,5,col,resultant,start,xval,yval);
XPRSmipoptimize(prob,"");
Further information
Piecewise linear constraints must be set up before solving the problem. They are converted to additional linear constraints, continuous variables and SOS2 constraints, with the exact formulation and number of added entities depending on the convexity of the piecewise linear function and some presolving steps that are applied.
Related topics
XPRSgetpwlcons, XPRSdelpwlcons.

Parent Topic Console and Library Functions

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