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

|Dear Friends,  

 

| Welcome to the spoken tutorial on '''Optimization of Linear Functions with Linear Constraints Using Scilab'''

 

| In this tutorial, We will learn  

|What is meant by '''Optimization?'''  

 

|And How to use Scilab function karmarkar for optimization.  

 

|Minimize or maximize a given '''objective function.'''  

 

|Which is also called as '''Cost function''' sometimes.

| By varying the decision variables

|The decision variables are varied subject to the pre-defined constraints.  

| '''Optimization''' is extensively used in majority of the engineering as well as non-engineering fields like  

 

|The Scilab function Karmarkar is used for  

|Optimizing the linear objective function  

 

||on the decision variables  

 

|| We will solve the following example using ''' karmarkar''' function:  

 

 

|for  '''two 'x' one plus 'x' two plus 'x' three  less than or equal to two.'''  

|Note that all the functions objective functions as well as constraints are linear  

 

||Before we solve the given problem go to '''scilab console''' and type  

 

| and '''press Enter.'''  

|The argument explaination, description and some examples in the '''help browser.'''  

 

| Close the '''help browser '''

 

| We will summarize the input and output arguments here  

|Out put arguments are ''' 'x' opt, 'f' opt, exitflag, iter, 'y' opt '''

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

 

|''' 'iter' ''': Is the number of iterations required to reach ''' 'x' opt.'''

|''' 'y' opt''' : is the structure containing the dual solution  

 

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

 

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

 

 

 

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

 

 

|''' 'maxiter' ''' : is the ''' Maximum''' number of iterations after which the output is returned.  

 

 

 

 

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

 

 

||''' 'ub'''' are the '''Upper bounds'''  of ''' 'x'. '''

 

||Now, we can now solve the given example in Scilab using ''' karmarkar''' function.  

 

|Go to the ''' scilab console and type'''  

 

 

 

|'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.

 

 

|And press Enter  

 

 

 

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

 

 

| And press '''Enter'''

 

| Type 'c' equals to open square bracket, minus three <semicolon> minus one <semicolon> minus three, close the square bracket.  

 

|And press ''' Enter'''

 

| Type 'lb' equals to open square bracket, zero <semicolon> zero <semicolon> zero, close the square bracket.  

|And press '''Enter'''

 

| 05:07

 

|Now clear the '''Scilab console using  clc command.'''

 

 

| 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. '''

 

 

| And Press '''enter'''

 

| Press Enter to continue the Display

 

 

 

| This will give the output as shown on the screen.

 

| Where '''xopt''' is the ''' optimal solution''' to the problem  

 

|'''fopt'''  is the value of the objective function calculated at optimum solution x is equal to '''xopt'''

 

|and number of iteration required to reach the optimum solution ''' xopt is 70'''  

 

|Please note that: it is mandatory to specify the input arguments in the same order.

 

|In which they have been listed above, while calling the function  

 

|In this tutorial, we learned  

 

|What is ''' Optimization?'''  

 

|Use of Scilab function karmarkar in optimization to solve linear problems.   

 

|To contact the scilab team, please write to ''' contact@scilab.in '''

 

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|This is Anuradha Amrutkar from IIT Bombay signing off.

 

| Thank you for joining Good Bye.