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MathGroup Archive 2007

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Re: Minimization with constraint expresses as CDF[] >=

  • To: mathgroup at smc.vnet.net
  • Subject: [mg72490] Re: [mg72474] Minimization with constraint expresses as CDF[] >=
  • From: "Chris Chiasson" <chris at chiasson.name>
  • Date: Mon, 1 Jan 2007 04:15:10 -0500 (EST)
  • References: <200612311007.FAA06784@smc.vnet.net>

The encoding in your message is not showing up correctly on my screen.
Would you mind using only the ASCII character set? I ask because I am
interested in your problem.

On 12/31/06, Pratim Vakish <pratim_usc at hotmail.com> wrote:
>
> Hello,
>
> I have the following optimization problem: a minimization subject to a few linear constraints and one chance constarint formulated using CDF[]
>
> Needs["Statistics`MultinormalDistribution`"];
> r={{0.01,-0.016},{-0.016,0.018}};
> ndist=MultinormalDistribution[{1,3},r];
> NMinimize[{2x1+x2,
> x1?0.8,
> x2?2.5,
> x1?0,
> x2?0,
> x1+x2==y,
> CDF[ndist,{x1,y}]?0.9,
> PrecisionGoal -> 3},
> {x1,x2,y}]
>
>
> I keep getting the following error message. I do not understand why. Any advice is welcome.
>
> NMinimize::"bcons":
> "The following constraints are not valid: y == x1 + x2, x1 ? 0, x2 ? 0, CDF[(MultinormalDistribution[({1, 3},({0.01,-0.016},{-0.016, 0.018}, {x1, y}] ? 0.9,
> x1 ? 0.8, x2 ? 2.5}.
> Constraints should be equalities, inequalities, or domain specifications involving the variables.
>
>
>
> ----------------------------------------
> > Date: Sat, 25 Nov 2006 09:53:24 -0500
> > From: hanlonr at cox.net
> > To: pratim_usc at hotmail.com; mathgroup at smc.vnet.net
> > Subject: Re: [mg71632] Numerical vaule of multinormal distribution
> >
> > Needs["Statistics`MultinormalDistribution`"];
> > r = {{0.8, 0.1}, {0.1, 0.2}};
> > ndist = MultinormalDistribution[{1, 0.4}, r];
> > CDF[ndist, {-1, 1}]
> >
> > 0.0124156
> >
> > I would guess that you tried to use to use CDF or MultinormalDistribution before loading the package. Evaluate after starting with a fresh kernel.
> >
> >
> > Bob Hanlon
> >
> > ---- Pratim Vakish <pratim_usc at hotmail.com> wrote:
> > >
> > > I have a basic question.
> > > I want toobtain the numerical value of the cumulative normal probability distribution function at some points.
> > > I have the following code to do this :
> > >
> > > Off[General::spell1];
> > > Needs["Statistics`MultinormalDistribution`"];
> > > r = {{0.8, 0.1}, {0.1, 0.2}};
> > > ndist = MultinormalDistribution[{1, 0.4}, r];
> > > CDF[ndist, {-1, 1}]
> > >
> > >
> > > The output I obtain is:
> > >
> > > CDF[MultinormalDistribution[{1, 0.4}, {{0.8, 0.1}, {0.1, 0.2}}], {-1, 1}]
> > >
> > > I would like to have the numerical value of this expression.
> > > How could I do?
> > >
> > >
> > > Pratim
> >
>
> _________________________________________________________________
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>


-- 
http://chris.chiasson.name/


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