Difference between revisions of "Scilab/C4/Optimization-Using-Karmarkar-Functions/English-timed"

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(Created page with '{| Border=1 || Time || Narration |- | 00.01 |Dear Friends, |- | 00.02 | Welcome to the spoken tutorial on '''Optimization of Linear Functions with Linear Constraints Using S…')
 
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{| Border=1
 
{| Border=1
  
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|'''Time'''
  
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|| Narration
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|'''Narration'''
  
 
|-
 
|-
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| 00:01
 
|Dear Friends,  
 
|Dear Friends,  
  
 
|-
 
|-
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| 00.02
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| 00:02
 
| Welcome to the spoken tutorial on '''Optimization of Linear Functions with Linear Constraints Using Scilab'''
 
| Welcome to the spoken tutorial on '''Optimization of Linear Functions with Linear Constraints Using Scilab'''
  
  
 
|-
 
|-
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| 00.10
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| 00:10
 
| In this tutorial, We will learn  
 
| In this tutorial, We will learn  
  
 
|-
 
|-
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|00.12
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|00:12
 
|What is meant by '''Optimization?'''  
 
|What is meant by '''Optimization?'''  
  
  
 
|-
 
|-
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|00.15
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|00:15
 
|And How to use Scilab function karmarkar for optimization.  
 
|And How to use Scilab function karmarkar for optimization.  
  
  
 
|-
 
|-
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| 00.20
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| 00:20
 
|'''Optimization''' means  
 
|'''Optimization''' means  
  
 
|-
 
|-
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|00.22
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|00:22
 
|Minimize or maximize a given '''objective function.'''  
 
|Minimize or maximize a given '''objective function.'''  
  
  
 
|-
 
|-
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| 00.26
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| 00:26
 
|Which is also called as '''Cost function''' sometimes.  
 
|Which is also called as '''Cost function''' sometimes.  
  
 
|-
 
|-
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| 00.30
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| 00:30
 
| By varying the decision variables
 
| By varying the decision variables
  
 
|-
 
|-
−
|00.33
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|00:33
 
|The decision variables are varied subject to the pre-defined constraints.  
 
|The decision variables are varied subject to the pre-defined constraints.  
  
 
|-
 
|-
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|00.38
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|00:38
 
|These constraints are also in the form of some functions of the variables.  
 
|These constraints are also in the form of some functions of the variables.  
  
 
|-
 
|-
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| 00.44
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| 00:44
 
| '''Optimization''' is extensively used in majority of the engineering as well as non-engineering fields like  
 
| '''Optimization''' is extensively used in majority of the engineering as well as non-engineering fields like  
  
 
|-
 
|-
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| 00.52
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| 00:52
 
| Economics  
 
| Economics  
  
 
|-
 
|-
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|00.54
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|00:54
 
|Control Theory and  
 
|Control Theory and  
  
 
|-
 
|-
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|00.56
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|00:56
 
| Operations & Research.  
 
| Operations & Research.  
  
 
|-
 
|-
  
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|00:58
  
 
|The Scilab function Karmarkar is used for  
 
|The Scilab function Karmarkar is used for  
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|-
 
|-
  
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|Optimizing the linear objective function  
 
|Optimizing the linear objective function  
  
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|-
 
|-
  
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| 01:05
  
 
|subject to linear constraints  
 
|subject to linear constraints  
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|-
 
|-
  
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| 01:07
 
||on the decision variables  
 
||on the decision variables  
  
 
|-
 
|-
  
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|01:10
  
 
|| We will solve the following example using ''' karmarkar'''  function:  
 
|| We will solve the following example using ''' karmarkar'''  function:  
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|-
 
|-
  
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|01.14
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|01:14
  
 
| Minimize '''minus three 'x' one minus 'x' two minus three 'x' three'''  
 
| Minimize '''minus three 'x' one minus 'x' two minus three 'x' three'''  
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|-
 
|-
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|01.19
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|01:19
 
|for  '''two 'x' one plus 'x' two plus 'x' three  less than or equal to two.'''  
 
|for  '''two 'x' one plus 'x' two plus 'x' three  less than or equal to two.'''  
 
   
 
   
 
|-
 
|-
  
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|01.26
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|01:26
  
 
|''' 'x' one plus two 'x' two plus three 'x' three  less than or equal to five.'''  
 
|''' 'x' one plus two 'x' two plus three 'x' three  less than or equal to five.'''  
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|-
 
|-
  
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|01.32
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|01:32
  
 
||'''two 'x' one plus two 'x' two plus 'x' three  less than or equal to six.'''  
 
||'''two 'x' one plus two 'x' two plus 'x' three  less than or equal to six.'''  
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|-
 
|-
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|01:36
 
|where ''' 'x' one 'x' two 'x' three''' are all '''greater than''' or '''equal to zero'''
 
|where ''' 'x' one 'x' two 'x' three''' are all '''greater than''' or '''equal to zero'''
  
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|-
 
|-
  
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| 01.42
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| 01:42
 
|Note that all the functions objective functions as well as constraints are linear  
 
|Note that all the functions objective functions as well as constraints are linear  
  
 
|-
 
|-
  
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|01.49
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|01:49
  
 
||Before we solve the given problem go to '''scilab console''' and type  
 
||Before we solve the given problem go to '''scilab console''' and type  
 
|-
 
|-
  
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|01.54
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|01:54
  
 
| '''help karmarkar'''
 
| '''help karmarkar'''
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|-
 
|-
  
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|01:57
  
 
| and '''press Enter.'''  
 
| and '''press Enter.'''  
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|-
 
|-
  
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| 01:59
  
 
||You can see the calling sequence of the argument.  
 
||You can see the calling sequence of the argument.  
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|-
 
|-
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| 02.03
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| 02:03
 
|The argument explaination, description and some examples in the '''help browser.'''  
 
|The argument explaination, description and some examples in the '''help browser.'''  
  
  
 
|-
 
|-
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|02.12
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|02:12
 
| Close the '''help browser '''
 
| Close the '''help browser '''
  
  
 
|-
 
|-
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|02.14
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|02:14
 
| We will summarize the input and output arguments here  
 
| We will summarize the input and output arguments here  
  
 
|-
 
|-
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| 02.19
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| 02:19
 
|Out put arguments are ''' 'x' opt, 'f' opt, exitflag, iter, 'y' opt '''
 
|Out put arguments are ''' 'x' opt, 'f' opt, exitflag, iter, 'y' opt '''
 
   
 
   
  
 
|-
 
|-
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|''' 'x' opt:''' is the optimum solution .  
 
|''' 'x' opt:''' is the optimum solution .  
  
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|-
 
|-
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| 02:28
 
|''''f' opt:'''  is the objective function value at '''optimum solution'''
 
|''''f' opt:'''  is the objective function value at '''optimum solution'''
  
  
 
|-
 
|-
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| 02.33
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| 02:33
 
|''' 'exitflag' ''': is the status of execution, it helps in identifying if the algorithm is converging or not.  
 
|''' 'exitflag' ''': is the status of execution, it helps in identifying if the algorithm is converging or not.  
  
 
|-
 
|-
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|02.41
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|02:41
 
|''' 'iter' ''': Is the number of iterations required to reach ''' 'x' opt.'''
 
|''' 'iter' ''': Is the number of iterations required to reach ''' 'x' opt.'''
  
 
|-
 
|-
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|02:46
 
|''' 'y' opt''' : is the structure containing the dual solution  
 
|''' 'y' opt''' : is the structure containing the dual solution  
  
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|-
 
|-
  
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| 02:49
  
 
|This gives the Lagrange multipliers.  
 
|This gives the Lagrange multipliers.  
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|-
 
|-
  
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| 02:53
 
||Input arguments are ''' 'Aeq' 'beq '    'c' 'x' zero 'rtolf 'gam' 'maxiter' 'outfun' 'A' 'b' 'lb' and 'ub' '''
 
||Input arguments are ''' 'Aeq' 'beq '    'c' 'x' zero 'rtolf 'gam' 'maxiter' 'outfun' 'A' 'b' 'lb' and 'ub' '''
 
'
 
'
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|-
 
|-
  
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|03:09
  
 
|| ''' 'Aeq' ''' : is the Matrix in the linear equality constraints.  
 
|| ''' 'Aeq' ''' : is the Matrix in the linear equality constraints.  
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|-
 
|-
  
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| 03.12
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| 03:12
 
| ''' 'beq' '''  :is the right hand side of the linear '''equality''' constraints.  
 
| ''' 'beq' '''  :is the right hand side of the linear '''equality''' constraints.  
  
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|-
 
|-
  
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| 03.17
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| 03:17
  
 
|''' 'c' ''' : is the '''Linear objective function''' co-efficients of  ''' 'x'. '''
 
|''' 'c' ''' : is the '''Linear objective function''' co-efficients of  ''' 'x'. '''
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|-
 
|-
  
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| 03.21
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| 03:21
  
 
| ''' 'x' zero''' : is the '''Initial guess .'''  
 
| ''' 'x' zero''' : is the '''Initial guess .'''  
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|-
 
|-
  
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|03.25
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|03:25
  
 
||''' rtolf ''': is Relative tolerance on ''' 'f' of 'x' is  equals to 'c' transpose multiplied by 'x'. '''
 
||''' rtolf ''': is Relative tolerance on ''' 'f' of 'x' is  equals to 'c' transpose multiplied by 'x'. '''
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|-
 
|-
  
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|03.34
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|03:34
  
 
|''' 'gam' ''' : is the Scaling factor.  
 
|''' 'gam' ''' : is the Scaling factor.  
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|-
 
|-
  
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| 03.36
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| 03:36
  
 
|''' 'maxiter' ''' : is the ''' Maximum''' number of iterations after which the output is returned.  
 
|''' 'maxiter' ''' : is the ''' Maximum''' number of iterations after which the output is returned.  
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|-
 
|-
  
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| 03.43
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| 03:43
  
 
|''' 'outfun' ''' : is the additional user-defined output functions .
 
|''' 'outfun' ''' : is the additional user-defined output functions .
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|-
 
|-
  
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| 03.47
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| 03:47
  
 
| ''' 'A' ''': is the Matrix of linear inequality constraints   
 
| ''' 'A' ''': is the Matrix of linear inequality constraints   
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|-
 
|-
  
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| 03.51
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| 03:51
  
 
| ''' 'b' ''': is the right hand side of the linear ''' inequality''' constraints.  
 
| ''' 'b' ''': is the right hand side of the linear ''' inequality''' constraints.  
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|-
 
|-
  
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| 03.55
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| 03:55
  
 
||''' 'lb' ''': is the ''' lowerbound''' of ''' 'x'.'''
 
||''' 'lb' ''': is the ''' lowerbound''' of ''' 'x'.'''
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|-
 
|-
  
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| 03.58
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| 03:58
  
 
||''' 'ub'''' are the '''Upper bounds'''  of ''' 'x'. '''
 
||''' 'ub'''' are the '''Upper bounds'''  of ''' 'x'. '''
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|-
 
|-
  
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| 04.02
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| 04:02
  
 
||Now, we can now solve the given example in Scilab using ''' karmarkar''' function.  
 
||Now, we can now solve the given example in Scilab using ''' karmarkar''' function.  
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|-
 
|-
  
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| 04.07
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| 04:07
  
 
|Go to the ''' scilab console and type'''  
 
|Go to the ''' scilab console and type'''  
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|-
 
|-
  
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| 04.11
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| 04:11
  
 
|'A' is equals to open square bracket, two <space> one <space> one <semicolon> one <space> two <space> three <semicolon> two <space> two <space> one, close the square bracket.  
 
|'A' is equals to open square bracket, two <space> one <space> one <semicolon> one <space> two <space> three <semicolon> two <space> two <space> one, close the square bracket.  
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|-
 
|-
  
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|04.26
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|04:26
  
 
|And press Enter  
 
|And press Enter  
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|-
 
|-
  
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| 04.28
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| 04:28
  
 
|similarly type, small 'b' equals to open square bracket, two <semicolon>five <semicolon> six, close the square bracket.  
 
|similarly type, small 'b' equals to open square bracket, two <semicolon>five <semicolon> six, close the square bracket.  
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|-
 
|-
  
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| 04:38
  
 
| And press '''Enter'''
 
| And press '''Enter'''
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|-
 
|-
  
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| 04.41
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| 04:41
  
 
| Type 'c' equals to open square bracket, minus three <semicolon> minus one <semicolon> minus three, close the square bracket.  
 
| Type 'c' equals to open square bracket, minus three <semicolon> minus one <semicolon> minus three, close the square bracket.  
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|-
 
|-
  
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| 04:53
  
 
|And press ''' Enter'''
 
|And press ''' Enter'''
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|-
 
|-
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| 04.55
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| 04:55
 
| Type 'lb' equals to open square bracket, zero <semicolon> zero <semicolon> zero, close the square bracket.  
 
| Type 'lb' equals to open square bracket, zero <semicolon> zero <semicolon> zero, close the square bracket.  
  
 
|-
 
|-
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| 05:05
 
|And press '''Enter'''
 
|And press '''Enter'''
  
 
|-
 
|-
  
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| 05:07
  
 
|Now clear the '''Scilab console using  clc command.'''
 
|Now clear the '''Scilab console using  clc command.'''
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|-
 
|-
  
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| Type ''' open square bracket, 'x' opt <comma> 'f' opt <comma> 'exitflag' <comma> iter, close the square bracket equals to karmarkar open parenthesis, open square bracket, close the square bracket <comma> open square bracket, close the square bracket <comma> 'c' <comma> open square bracket, close the square bracket <comma> open square bracket, close the square bracket <comma> open square bracket, close the square bracket <comma> open square bracket, close the square bracket <comma> open square bracket, close the square bracket <comma> capital 'A' <comma> 'small b' <comma> 'lb', close the round bracket. '''
 
| Type ''' open square bracket, 'x' opt <comma> 'f' opt <comma> 'exitflag' <comma> iter, close the square bracket equals to karmarkar open parenthesis, open square bracket, close the square bracket <comma> open square bracket, close the square bracket <comma> 'c' <comma> open square bracket, close the square bracket <comma> open square bracket, close the square bracket <comma> open square bracket, close the square bracket <comma> open square bracket, close the square bracket <comma> open square bracket, close the square bracket <comma> capital 'A' <comma> 'small b' <comma> 'lb', close the round bracket. '''
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|-
 
|-
  
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| 06:09
  
 
| And Press '''enter'''
 
| And Press '''enter'''
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|-
 
|-
  
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| 06:11
  
 
| Press Enter to continue the Display
 
| Press Enter to continue the Display
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|-
 
|-
  
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| This will give the output as shown on the screen.  
 
| This will give the output as shown on the screen.  
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|-
 
|-
  
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| 06:18
  
 
| Where '''xopt'''  is the ''' optimal solution''' to the problem  
 
| Where '''xopt'''  is the ''' optimal solution''' to the problem  
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|-
 
|-
  
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| 06:23
  
 
|'''fopt'''  is the value of the objective function calculated at optimum solution x is equal to '''xopt'''
 
|'''fopt'''  is the value of the objective function calculated at optimum solution x is equal to '''xopt'''
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|-
 
|-
  
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|and number of iteration required to reach the optimum solution ''' xopt is 70'''  
 
|and number of iteration required to reach the optimum solution ''' xopt is 70'''  
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|-
 
|-
  
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|Please note that: it is mandatory to specify the input arguments in the same order.  
 
|Please note that: it is mandatory to specify the input arguments in the same order.  
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|-
 
|-
  
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|In which they have been listed above, while calling the function  
 
|In which they have been listed above, while calling the function  
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|-
 
|-
  
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|In this tutorial, we learned  
 
|In this tutorial, we learned  
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|-
 
|-
  
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| 06:53
  
 
|What is ''' Optimization?'''  
 
|What is ''' Optimization?'''  
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|-
 
|-
  
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|Use of Scilab function karmarkar in optimization to solve linear problems.   
 
|Use of Scilab function karmarkar in optimization to solve linear problems.   
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|-
 
|-
  
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|To contact the scilab team, please write to ''' contact@scilab.in '''
 
|To contact the scilab team, please write to ''' contact@scilab.in '''
  
  
 
|-
 
|-
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|07.08
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|07:08
 
| Watch the video available at the following link
 
| Watch the video available at the following link
  
 
|-
 
|-
  
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| 07:10
  
 
| It summarises the Spoken Tutorial project  
 
| It summarises the Spoken Tutorial project  
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|-
 
|-
  
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||If you do not have good bandwidth, you can download and watch it  
 
||If you do not have good bandwidth, you can download and watch it  
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|-
 
|-
  
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||The spoken tutorial project Team
 
||The spoken tutorial project Team
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|-
  
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||Conducts workshops using spoken tutorials  
 
||Conducts workshops using spoken tutorials  
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|-
  
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||Gives certificates to those who pass an online test  
 
||Gives certificates to those who pass an online test  
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|-
 
|-
  
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|07:27
  
 
||For more details, please write to contact@spoken-tutorial.org  
 
||For more details, please write to contact@spoken-tutorial.org  
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|-
 
|-
  
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|Spoken Tutorial Project is a part of the Talk to a Teacher project  
 
|Spoken Tutorial Project is a part of the Talk to a Teacher project  
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|-
 
|-
  
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| It is supported by the National Mission on Eduction through ICT, MHRD, Government of India.  
 
| It is supported by the National Mission on Eduction through ICT, MHRD, Government of India.  
 
|-
 
|-
  
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|More information on this mission is available at spoken-tutorial.org/NMEICT-Intro
 
|More information on this mission is available at spoken-tutorial.org/NMEICT-Intro
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|-
 
|-
  
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|This is Anuradha Amrutkar from IIT Bombay signing off.
 
|This is Anuradha Amrutkar from IIT Bombay signing off.
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| Thank you for joining Good Bye.
 
| Thank you for joining Good Bye.

Revision as of 10:46, 11 July 2014

Time Narration
00:01 Dear Friends,
00:02 Welcome to the spoken tutorial on Optimization of Linear Functions with Linear Constraints Using Scilab


00:10 In this tutorial, We will learn
00:12 What is meant by Optimization?


00:15 And How to use Scilab function karmarkar for optimization.


00:20 Optimization means
00:22 Minimize or maximize a given objective function.


00:26 Which is also called as Cost function sometimes.
00:30 By varying the decision variables
00:33 The decision variables are varied subject to the pre-defined constraints.
00:38 These constraints are also in the form of some functions of the variables.
00:44 Optimization is extensively used in majority of the engineering as well as non-engineering fields like
00:52 Economics
00:54 Control Theory and
00:56 Operations & Research.
00:58 The Scilab function Karmarkar is used for
01:01 Optimizing the linear objective function


01:05 subject to linear constraints


01:07 on the decision variables
01:10 We will solve the following example using karmarkar function:


01:14 Minimize minus three 'x' one minus 'x' two minus three 'x' three


01:19 for two 'x' one plus 'x' two plus 'x' three less than or equal to two.
01:26 'x' one plus two 'x' two plus three 'x' three less than or equal to five.


01:32 two 'x' one plus two 'x' two plus 'x' three less than or equal to six.


01:36 where 'x' one 'x' two 'x' three are all greater than or equal to zero


01:42 Note that all the functions objective functions as well as constraints are linear
01:49 Before we solve the given problem go to scilab console and type
01:54 help karmarkar
01:57 and press Enter.
01:59 You can see the calling sequence of the argument.


02:03 The argument explaination, description and some examples in the help browser.


02:12 Close the help browser


02:14 We will summarize the input and output arguments here
02:19 Out put arguments are 'x' opt, 'f' opt, exitflag, iter, 'y' opt


02:25 'x' opt: is the optimum solution .


02:28 'f' opt: is the objective function value at optimum solution


02:33 'exitflag' : is the status of execution, it helps in identifying if the algorithm is converging or not.
02:41 'iter' : Is the number of iterations required to reach 'x' opt.
02:46 'y' opt : is the structure containing the dual solution


02:49 This gives the Lagrange multipliers.



02:53 Input arguments are 'Aeq' 'beq ' 'c' 'x' zero 'rtolf 'gam' 'maxiter' 'outfun' 'A' 'b' 'lb' and 'ub'

'


03:09 'Aeq'  : is the Matrix in the linear equality constraints.


03:12 'beq'  :is the right hand side of the linear equality constraints.


03:17 'c'  : is the Linear objective function co-efficients of 'x'.


03:21 'x' zero : is the Initial guess .
03:25 rtolf : is Relative tolerance on 'f' of 'x' is equals to 'c' transpose multiplied by 'x'.


03:34 'gam'  : is the Scaling factor.
03:36 'maxiter'  : is the Maximum number of iterations after which the output is returned.



03:43 'outfun'  : is the additional user-defined output functions .


03:47 'A' : is the Matrix of linear inequality constraints
03:51 'b' : is the right hand side of the linear inequality constraints.
03:55 'lb' : is the lowerbound of 'x'.


03:58 'ub' are the Upper bounds of 'x'.
04:02 Now, we can now solve the given example in Scilab using karmarkar function.
04:07 Go to the scilab console and type


04:11 'A' is equals to open square bracket, two <space> one <space> one <semicolon> one <space> two <space> three <semicolon> two <space> two <space> one, close the square bracket.


04:26 And press Enter


04:28 similarly type, small 'b' equals to open square bracket, two <semicolon>five <semicolon> six, close the square bracket.


04:38 And press Enter
04:41 Type 'c' equals to open square bracket, minus three <semicolon> minus one <semicolon> minus three, close the square bracket.
04:53 And press Enter


04:55 Type 'lb' equals to open square bracket, zero <semicolon> zero <semicolon> zero, close the square bracket.
05:05 And press Enter
05:07 Now clear the Scilab console using clc command.


05:12 Type open square bracket, 'x' opt <comma> 'f' opt <comma> 'exitflag' <comma> iter, close the square bracket equals to karmarkar open parenthesis, open square bracket, close the square bracket <comma> open square bracket, close the square bracket <comma> 'c' <comma> open square bracket, close the square bracket <comma> open square bracket, close the square bracket <comma> open square bracket, close the square bracket <comma> open square bracket, close the square bracket <comma> open square bracket, close the square bracket <comma> capital 'A' <comma> 'small b' <comma> 'lb', close the round bracket.


06:09 And Press enter
06:11 Press Enter to continue the Display


06:14 This will give the output as shown on the screen.
06:18 Where xopt is the optimal solution to the problem
06:23 fopt is the value of the objective function calculated at optimum solution x is equal to xopt
06:32 and number of iteration required to reach the optimum solution xopt is 70
06:39 Please note that: it is mandatory to specify the input arguments in the same order.
06:46 In which they have been listed above, while calling the function
06:51 In this tutorial, we learned
06:53 What is Optimization?
06:55 Use of Scilab function karmarkar in optimization to solve linear problems.


07:01 To contact the scilab team, please write to contact@scilab.in


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07:53 This is Anuradha Amrutkar from IIT Bombay signing off.
07:57 Thank you for joining Good Bye.

Contributors and Content Editors

Gaurav, PoojaMoolya, Sandhya.np14

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