Quickguide PIECE-WISE LINEAR Problem: Difference between revisions
(Created page with "{{Part Of Manual|title=the Quickguide Manual|link=Quickguide}} The general formulation in TOMLAB for a piece-wise linear programming problem is: <math> \begin{ar...") |
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s/t & \begin{array}{lcccl} | s/t & \begin{array}{lcccl} | ||
x_{L} & \leq & x & \leq & x_{U}, \\ | x_{L} & \leq & x & \leq & x_{U}, \\ | ||
b_{L} & \leq & A x & \leq & b_{U}, ~x_{j} \in \ | b_{L} & \leq & A x & \leq & b_{U}, ~x_{j} \in \mathbb{N}\ ~~\forall j \in $I$ \\\end{array}\end{array} | ||
</math> | </math> | ||
where <math>c, x, x_L, x_U \in \ | where <math>c, x, x_L, x_U \in \mathbb{R}^n</math>, <math>A \in \mathbb{R}^{m_1 | ||
\times n}</math>, and <math>b_L,b_U \in \ | \times n}</math>, and <math>b_L,b_U \in \mathbb{R}^{m_1}</math>. The variables <math>x | ||
\in I</math>, the index subset of <math>1,...,n</math> are restricted to be integers. | \in I</math>, the index subset of <math>1,...,n</math> are restricted to be integers. | ||
Equality constraints are defined by setting the lower bound equal to | Equality constraints are defined by setting the lower bound equal to | ||
Latest revision as of 18:35, 17 January 2012
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This page is part of the Quickguide Manual. See Quickguide. |
The general formulation in TOMLAB for a piece-wise linear programming problem is:
where , , and . The variables , the index subset of are restricted to be integers. Equality constraints are defined by setting the lower bound equal to the upper bound, i.e. for constraint : . A subset of the variables 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.
