       Minimization with constraint expresses as CDF[] >=

• To: mathgroup at smc.vnet.net
• Subject: [mg72474] Minimization with constraint expresses as CDF[] >=
• From: Pratim Vakish <pratim_usc at hotmail.com>
• Date: Sun, 31 Dec 2006 05:07:00 -0500 (EST)

```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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