Quickguide PIECE-WISE LINEAR Problem

This page is part of the Quickguide Manual. See Quickguide.

The general formulation in TOMLAB for a piece-wise linear programming problem is:

${\begin{array}{ll}\min \limits _{x}&f(x)={\frac {1}{2}}x^{T}Fx+c^{T}x\\&\\s/t&{\begin{array}{lcccl}x_{L}&\leq &x&\leq &x_{U},\\b_{L}&\leq &Ax&\leq &b_{U},~x_{j}\in \mathbb {N} \ ~~\forall j\in \$I\$\\\end{array}}\end{array}}$

where $c,x,x_{L},x_{U}\in \mathbb {R} ^{n}$, $A\in \mathbb {R} ^{m_{1}\times n}$, and $b_{L},b_{U}\in \mathbb {R} ^{m_{1}}$. The variables $x\in I$, the index subset of $1,...,n$ are restricted to be integers. Equality constraints are defined by setting the lower bound equal to the upper bound, i.e. for constraint $i$: $b_{L}(i)=b_{U}(i)$. A subset of the variables $x$ are piece-wise linear.

Solving piece-wise linear problem is mainly recommended by using TOMLAB /CPLEX or similar solver.

The following file defines a test case in TOMLAB. It is possible to use two syntax variations when defining the problem (see help addPwLinFunc for more information).

File: tomlab/quickguide/piecewiseQG.m

Open the file for viewing, and execute piecewiseQG in Matlab.