Re: FindMinimum during NMimimize

• To: mathgroup at smc.vnet.net
• Subject: [mg65606] Re: FindMinimum during NMimimize
• From: dh <dh at metrohm.ch>
• Date: Tue, 11 Apr 2006 04:04:11 -0400 (EDT)
• References: <e15el3\$2ri\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```
Hi Mario,

if I understand you correctly, then you want do calculate the distance

of a point r0 from a line L1. This can be calculated with much less effort.

Imagine a vector v from a point r1 on the line L1 to the given point r0.

If we then project this vector on a line L2 perpendicular to L1, the

length of the projection is the searched distance. To make life easier

we choose a unit vector u along line L2. The distance can then be got by

the scalar product v.u:

given line: y1=c0+c1 x1

r0: {x0,y0}

r1: {x1,y1} if we choose x1==0, this becames r1={0,c0}

vector parallel to L1: {1,c1}

vector perpendicular to L1: {-c1,1} (to check, take the scalar product)

Unit vector perpendicular to L1: u={-c1,1}/Sqrt[1+c1^2]

vector from r1 to r0: r0-r1= {x0,y0}-{0,c0} ={x0,y0-c0}

distance= Abs[ {x0,y0-c0}.{-c1,1}/Sqrt[1+c1^2]  ]

Daniel

mfific at gmail.com wrote:

> Dear all,

>

> Math ver 5.0

> Here is my problem:

>

> discra[x_,slopex_,intx_]:=x*slopex+intx

>

> distanceOverX[ma1_,ma2_,slopex_,intx_]:=

> FindMinimum[Sqrt[(ma1-x)^2+(ma2-discra[x,slopex,intx])^2],{x,10,20}][[1]]

>

> NMinimize[{(distanceOverX[1,1,0,intx]-100)^2,0<intx<10},

>

>

> I defined a function distanceOverX above that includes FindMinimum for

> x variable. And that function works fine by itslef: as an otput I take

> the minimized value.

>

> But when I used distanceOverXfunction for finding global Min using

> NMinimize, I got the error which indicates that FindMinimum could not

> do the job:

> for example: The function value ....is not a number at {x}={10}....

>

> I would appreciate for a suggestion how to unlock that  problem.

> (Note that for NMinmize I let only one variable (intx) from the

> function distanceOverX to be free parameter while other values are

> provided)

>

> thank you very much,

>

> Mario Fific

>

> Cognitive Psychology and Cognitive Science

> Indiana University

>

```

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