extreme

Purpose

Compute an extreme point of this set in the given direction.

Syntax

s = S.extreme(x)
s = extreme(S, x)

Description

Compute an extreme point of this set in the direction given by the point x.

Input Arguments

S

A convex set described as YSet object.

Class: YSet

x

A point given as vector. Note that for YSet with symmetric matrix variable, the point x must be given as vector with symmetric terms.

Class: double

Output Arguments

s

The output structure with the information about the extreme point and the exit status from the optimization.

Class: struct

s.exitflag

Exit status from the optimization, i.e. an integer value that informs if the result was feasible (1), or otherwise (different from 1).

Class: double

s.how

A string that informs if the result was feasible ('ok'), or if any problem appeared through optimization.

Class: char

s.x

Computed extreme point that lies on the boundary of the set S.

Class: double

s.supp

The support of this set in the direction x which represents the optimal value of the objective function in the optimization problem ../../../../../../fig/mpt/modules/geometry/sets/@YSet/extreme1.png.

Class: double

Example(s)

Example 1

Create a set in 2D as intersection of the following inequalities.
x = sdpvar(2,1);

F = [ [-3 0.3;0.1 -1;-0.1 2]*x<=[0.8;2.1;1.5] ];

F = [F; 0.3*x'*x-4*x(1)+2*x(2)<=0.1];

S = YSet(x,F);
Compute the extreme point in the direction of the point v=[0;2].
v = [6;0];

s = S.extreme(v);
 The computed extreme point is lying the edge of the set. We can plot the set and the point s.x. 
 S.plot; hold on; text(s.x(1),s.x(2),'\bf x'); 
Plotting...
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../../../../../../fig/mpt/modules/geometry/sets/@YSet/extreme_img_1.png

See Also

contains, project, shoot


© 2010-2013 Colin Neil Jones: EPF Lausanne, colin.jones@epfl.ch

© 2010-2013 Martin Herceg: ETH Zurich, herceg@control.ee.ethz.ch