Re: [Help-glpk] Can I simulate step function in GLPK?

[xiaomi]

Thanks, Michael. I am sorry there are several typo in my original 
statement. Let me recify it as follows:
for example: step function y=u(5);
maxmize y
y<=M(x-5) , where M is a large number to simulate sharp slope.
y<=1;

The only wired thing is that when x<5, y will be y  <= a number that is 
negative. However if y  is  nongative as default, can this property 
restrict y to be 0 when x<5? (without binary)





Michael Hennebry :
> On Wed, 1 Sep 2010, xiaomi wrote:
>
> > I am considering to use the property that the result of GLPK is
> > non-negative to simulate step function as follows:
> > for example: step function y=u(5);
> > minimize y
> > y<=M(x-5) , where M is a large number to simulate sharp slope.
> > y<=1;
> >
> > It seems to imply that when y<=5, y>=M(x-5) && y>=0.
> > Does that work(fast?)? And is GLPK default to be non-negative result?
>
> Not for x> 5.
> In that case, y< 0.
> Note that neither of you constraints is good for minimizing y.
>
> I gather that you want to allow y to be 0 only in the range [0, 5]
> and 1 only in the range [5, H], where H is an upper bound on x.
>        ________
>  _____|
>
> The convex hull is a quadralateral.
> Two of the sides are y>=0 and y<=1.
> I'll leave the other two as an exercise for the reader.
> Be sure to make y binary.
> If you are minimizing y, you can omit two of the sides.