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Findminimum of Integral

FindMinimum, NMinimize, etc. with external processIntegration does not give real valueFindMinimum function does not produce minimum from near pointFindMinimum and WhenEventSimplifying Expressions for FindMinimumIssues with methods of FindMinimumCan you run FindMinimum excluding imaginary results?FindMinimum yields result, but still issues MachinePrecision digits errorFindMinimum Error - cvec: Constrained optimization is only supported with scalar valued variablesWhy is my integral not being evaluated?

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2

$begingroup$

I am trying to find the value of $u$ that minimizes the following expression:

q = 1 - Exp[-u/b];

expr = Log[(1/(2 + b)) (1/(1 - q + q^2)) (q + 

       q^2 + (1 - q)^2 Exp[-u/2])/0.3553];   (*SEC BER equation *)

FindMinimum[Integrate[expr, {b, 1, 10}], {u, 0, 10}]

However, it does not yield any output. What's wrong with the code?

numerical-integration mathematical-optimization

share|improve this question

asked 9 hours ago

jhon_wickjhon_wick

17966 bronze badges

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  You may want to replace = by :=.
  $endgroup$
  – A.G.
  9 hours ago
  

  
  
  
  

add a comment | 

2

$begingroup$

I am trying to find the value of $u$ that minimizes the following expression:

q = 1 - Exp[-u/b];

expr = Log[(1/(2 + b)) (1/(1 - q + q^2)) (q + 

       q^2 + (1 - q)^2 Exp[-u/2])/0.3553];   (*SEC BER equation *)

FindMinimum[Integrate[expr, {b, 1, 10}], {u, 0, 10}]

However, it does not yield any output. What's wrong with the code?

numerical-integration mathematical-optimization

share|improve this question

asked 9 hours ago

jhon_wickjhon_wick

17966 bronze badges

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  You may want to replace = by :=.
  $endgroup$
  – A.G.
  9 hours ago
  

  
  
  
  

add a comment | 

$begingroup$

I am trying to find the value of $u$ that minimizes the following expression:

q = 1 - Exp[-u/b];

expr = Log[(1/(2 + b)) (1/(1 - q + q^2)) (q + 

       q^2 + (1 - q)^2 Exp[-u/2])/0.3553];   (*SEC BER equation *)

FindMinimum[Integrate[expr, {b, 1, 10}], {u, 0, 10}]

However, it does not yield any output. What's wrong with the code?

numerical-integration mathematical-optimization

share|improve this question

asked 9 hours ago

jhon_wickjhon_wick

17966 bronze badges

$endgroup$

q = 1 - Exp[-u/b];

expr = Log[(1/(2 + b)) (1/(1 - q + q^2)) (q + 

       q^2 + (1 - q)^2 Exp[-u/2])/0.3553];   (*SEC BER equation *)

FindMinimum[Integrate[expr, {b, 1, 10}], {u, 0, 10}]

share|improve this question

asked 9 hours ago

jhon_wickjhon_wick

17966 bronze badges

share|improve this question

asked 9 hours ago

jhon_wickjhon_wick

17966 bronze badges

asked 9 hours ago

jhon_wickjhon_wick

17966 bronze badges

asked 9 hours ago

jhon_wickjhon_wick

17966 bronze badges

1 Answer
1

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oldest

votes

6

$begingroup$

You can do something like this.

Clear[expr];

q = 1 - Exp[-u/b];

expr[u_?NumericQ] := 

 NIntegrate[

  Log[(1/(2 + b)) (1/(1 - q + q^2)) (q + q^2 + (1 - q)^2 Exp[-u/2])/0.3553], {b, 1, 10}];

Now easy to optimize.

FindMinimum[expr[u], {u, 0, 10}]

{-10.5871, {u -> 1.2105}}

share|improve this answer

answered 9 hours ago

PlatoManiacPlatoManiac

12.1k22 gold badges2929 silver badges6868 bronze badges

$endgroup$

add a comment | 

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6

$begingroup$

You can do something like this.

Clear[expr];

q = 1 - Exp[-u/b];

expr[u_?NumericQ] := 

 NIntegrate[

  Log[(1/(2 + b)) (1/(1 - q + q^2)) (q + q^2 + (1 - q)^2 Exp[-u/2])/0.3553], {b, 1, 10}];

Now easy to optimize.

FindMinimum[expr[u], {u, 0, 10}]

{-10.5871, {u -> 1.2105}}

share|improve this answer

answered 9 hours ago

PlatoManiacPlatoManiac

12.1k22 gold badges2929 silver badges6868 bronze badges

$endgroup$

add a comment | 

6

$begingroup$

You can do something like this.

Clear[expr];

q = 1 - Exp[-u/b];

expr[u_?NumericQ] := 

 NIntegrate[

  Log[(1/(2 + b)) (1/(1 - q + q^2)) (q + q^2 + (1 - q)^2 Exp[-u/2])/0.3553], {b, 1, 10}];

Now easy to optimize.

FindMinimum[expr[u], {u, 0, 10}]

{-10.5871, {u -> 1.2105}}

share|improve this answer

answered 9 hours ago

PlatoManiacPlatoManiac

12.1k22 gold badges2929 silver badges6868 bronze badges

$endgroup$

add a comment | 

$begingroup$

You can do something like this.

Clear[expr];

q = 1 - Exp[-u/b];

expr[u_?NumericQ] := 

 NIntegrate[

  Log[(1/(2 + b)) (1/(1 - q + q^2)) (q + q^2 + (1 - q)^2 Exp[-u/2])/0.3553], {b, 1, 10}];

Now easy to optimize.

FindMinimum[expr[u], {u, 0, 10}]

{-10.5871, {u -> 1.2105}}

share|improve this answer

answered 9 hours ago

PlatoManiacPlatoManiac

12.1k22 gold badges2929 silver badges6868 bronze badges

$endgroup$

Clear[expr];

q = 1 - Exp[-u/b];

expr[u_?NumericQ] := 

 NIntegrate[

  Log[(1/(2 + b)) (1/(1 - q + q^2)) (q + q^2 + (1 - q)^2 Exp[-u/2])/0.3553], {b, 1, 10}];

FindMinimum[expr[u], {u, 0, 10}]

share|improve this answer

answered 9 hours ago

PlatoManiacPlatoManiac

12.1k22 gold badges2929 silver badges6868 bronze badges

answered 9 hours ago

PlatoManiacPlatoManiac

12.1k22 gold badges2929 silver badges6868 bronze badges

answered 9 hours ago

PlatoManiacPlatoManiac

12.1k22 gold badges2929 silver badges6868 bronze badges