piecewise.py File Reference

several approaches for solving problems with piecewise linear functions. More...

Go to the source code of this file.

Functions
def	mult_selection (model, a, b)
def	convex_comb_sos (model, a, b)
def	convex_comb_dis (model, a, b)
def	gray (i)
def	convex_comb_dis_log (model, a, b)
def	convex_comb_agg (model, a, b)
def	convex_comb_agg_log (model, a, b)

Variables
list	a = [ -10, 10, 15, 25, 30, 35, 40, 45, 50, 55, 60, 70]
list	b = [ -20,-20, 15, -21, 0, 50, 18, 0, 15, 24, 10, 15]
	model = Model("multiple selection")
	X
	Y
	z
	u = model.addVar(vtype="C", name="u")
	A = model.addCons(3*X + 4*Y <= 250, "A")
	B = model.addCons(7*X - 2*Y + 3*u == 170, "B")
	w

Detailed Description

several approaches for solving problems with piecewise linear functions.

Definition in file piecewise.py.

Function Documentation

def piecewise.convex_comb_agg	(		model,
			a,
			b
	)

convex_comb_agg -- add piecewise relation convex combination formulation -- non-disaggregated.
Parameters:
    - model: a model where to include the piecewise linear relation
    - a[k]: x-coordinate of the k-th point in the piecewise linear relation
    - b[k]: y-coordinate of the k-th point in the piecewise linear relation
Returns the model with the piecewise linear relation on added variables X, Y, and z.

Definition at line 149 of file piecewise.py.

def piecewise.convex_comb_agg_log	(		model,
			a,
			b
	)

convex_comb_agg_log -- add piecewise relation with a logarithmic number of binary variables
using the convex combination formulation -- non-disaggregated.
Parameters:
    - model: a model where to include the piecewise linear relation
    - a[k]: x-coordinate of the k-th point in the piecewise linear relation
    - b[k]: y-coordinate of the k-th point in the piecewise linear relation
Returns the model with the piecewise linear relation on added variables X, Y, and z.

Definition at line 178 of file piecewise.py.

def piecewise.convex_comb_dis	(		model,
			a,
			b
	)

convex_comb_dis -- add piecewise relation with convex combination formulation
Parameters:
    - model: a model where to include the piecewise linear relation
    - a[k]: x-coordinate of the k-th point in the piecewise linear relation
    - b[k]: y-coordinate of the k-th point in the piecewise linear relation
Returns the model with the piecewise linear relation on added variables X, Y, and z.

Definition at line 73 of file piecewise.py.

def piecewise.convex_comb_dis_log	(		model,
			a,
			b
	)

convex_comb_dis_log -- add piecewise relation with a logarithmic number of binary variables
using the convex combination formulation.
Parameters:
    - model: a model where to include the piecewise linear relation
    - a[k]: x-coordinate of the k-th point in the piecewise linear relation
    - b[k]: y-coordinate of the k-th point in the piecewise linear relation
Returns the model with the piecewise linear relation on added variables X, Y, and z.

Definition at line 105 of file piecewise.py.

def piecewise.convex_comb_sos	(		model,
			a,
			b
	)

convex_comb_sos -- add piecewise relation with gurobi's SOS constraints
Parameters:
    - model: a model where to include the piecewise linear relation
    - a[k]: x-coordinate of the k-th point in the piecewise linear relation
    - b[k]: y-coordinate of the k-th point in the piecewise linear relation
Returns the model with the piecewise linear relation on added variables X, Y, and z.

Definition at line 49 of file piecewise.py.

def piecewise.gray

(

i

)

returns i^int(i/2)

Definition at line 100 of file piecewise.py.

def piecewise.mult_selection	(		model,
			a,
			b
	)

mult_selection -- add piecewise relation with multiple selection formulation
Parameters:
    - model: a model where to include the piecewise linear relation
    - a[k]: x-coordinate of the k-th point in the piecewise linear relation
    - b[k]: y-coordinate of the k-th point in the piecewise linear relation
Returns the model with the piecewise linear relation on added variables X, Y, and z.

Definition at line 18 of file piecewise.py.