mpt_ineq2eq

Purpose

Detects inequality constraints which form equalities

Syntax

[An, bn, Ae, be, ind_e] = mpt_ineq2eq(A, b, tol)

Description

For a system of inequalities ../../../fig/mpt/utils/mpt_ineq2eq1.png, this function detects and returns those inequality constraints which form equalities. For instance: A = [1; -1; 1]; b = [1; -1; 2]; The output will lead: An = [-1]; bn = [2]; Ae = [1]; be = 1; such that the original problem can be rewritten as:

../../../fig/mpt/utils/mpt_ineq2eq15.png

The algorithm works up to specified tolerance tol.

Input Arguments

A

Matrix of inequality constraints in ../../../fig/mpt/utils/mpt_ineq2eq2.png

Class: double

b

Right hand side of inequalities in ../../../fig/mpt/utils/mpt_ineq2eq3.png

Class: double

tol

Working precision of the algorithm.

Class: double

Default: MPTOPTIONS.abs_tol

Output Arguments

An

Matrix of new inequality constraints ../../../fig/mpt/utils/mpt_ineq2eq4.png

Class: double

bn

Right hand side of new inequality constraints in ../../../fig/mpt/utils/mpt_ineq2eq5.png

Class: double

Ae

Matrix of equality constraints ../../../fig/mpt/utils/mpt_ineq2eq6.png

Class: double

be

Right hand side of equality constraints in ../../../fig/mpt/utils/mpt_ineq2eq7.png

Class: double

ind_e

Rows of ../../../fig/mpt/utils/mpt_ineq2eq8.png, ../../../fig/mpt/utils/mpt_ineq2eq9.png that create a pair of double sided inequalities, sorted in columns.

Class: double

Example(s)

Example 1

A system of inequalities ../../../fig/mpt/utils/mpt_ineq2eq10.png, ../../../fig/mpt/utils/mpt_ineq2eq11.png, ../../../fig/mpt/utils/mpt_ineq2eq12.png contains one equality constraint ../../../fig/mpt/utils/mpt_ineq2eq13.png written as double-sided inequality. The corresponding matrix form of inequalities ../../../fig/mpt/utils/mpt_ineq2eq14.png is built by
A = [1; -1; 1];

b = [1; -1; 2];
 To detect the equality, we use mpt_ineq2eq function
[An, bn, Ae, be] = mpt_ineq2eq(A,b)
An =

     1


bn =

     2


Ae =

     1


be =

     1

See Also

polyhedron


© 2003-2013 Michal Kvasnica: STU Bratislava, michal.kvasnica@stuba.sk

© 2006 Johan Loefberg: ETH Zurich , loefberg@control.ee.ethz.ch