Scilab/C4/Optimization-Using-Karmarkar-Functions/English-timed
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| Time | Narration |
| 00.01 | Dear Friends, |
| 00.02 | Welcome to the spoken tutorial on Optimization of Linear Functions with Linear Constraints Using Scilab
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| 00.10 | In this tutorial, We will learn |
| 00.12 | What is meant by Optimization?
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| 00.15 | And How to use Scilab function karmarkar for optimization.
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| 00.20 | Optimization means |
| 00.22 | Minimize or maximize a given objective function.
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| 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
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| 01.05 | subject to linear constraints
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| 01.07 | on the decision variables |
| 01.10 | We will solve the following example using karmarkar function:
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| 01.14 | Minimize minus three 'x' one minus 'x' two minus three 'x' three
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| 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.
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| 01.32 | two 'x' one plus two 'x' two plus 'x' three less than or equal to six.
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| 01.36 | where 'x' one 'x' two 'x' three are all greater than or equal to zero
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| 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.
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| 02.03 | The argument explaination, description and some examples in the help browser.
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| 02.12 | Close the help browser
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| 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
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| 02.25 | 'x' opt: is the optimum solution .
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| 02.28 | 'f' opt: is the objective function value at optimum solution
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| 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
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| 02.49 | This gives the Lagrange multipliers.
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| 02.53 | Input arguments are 'Aeq' 'beq ' 'c' 'x' zero 'rtolf 'gam' 'maxiter' 'outfun' 'A' 'b' 'lb' and 'ub'
'
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| 03.09 | 'Aeq' : is the Matrix in the linear equality constraints.
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| 03.12 | 'beq' :is the right hand side of the linear equality constraints.
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| 03.17 | 'c' : is the Linear objective function co-efficients of 'x'.
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| 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'.
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| 03.34 | 'gam' : is the Scaling factor. |
| 03.36 | 'maxiter' : is the Maximum number of iterations after which the output is returned.
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| 03.43 | 'outfun' : is the additional user-defined output functions .
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| 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'.
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| 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
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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.
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| 04.26 | And press Enter
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| 04.28 | similarly type, small 'b' equals to open square bracket, two <semicolon>five <semicolon> six, close the square bracket.
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| 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
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| 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.
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| 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.
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| 06.09 | And Press enter |
| 06.11 | Press Enter to continue the Display
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| 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.
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| 07.01 | To contact the scilab team, please write to contact@scilab.in
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| 07.08 | Watch the video available at the following link |
| 07.10 | It summarises the Spoken Tutorial project
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| 07.14 | If you do not have good bandwidth, you can download and watch it |
| 07.18 | The spoken tutorial project Team |
| 07.20 | Conducts workshops using spoken tutorials
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| 07.23 | Gives certificates to those who pass an online test
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| 07.27 | For more details, please write to contact@spoken-tutorial.org
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| 07.34 | Spoken Tutorial Project is a part of the Talk to a Teacher project
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| 07.37 | It is supported by the National Mission on Eduction through ICT, MHRD, Government of India. |
| 07.44 | More information on this mission is available at spoken-tutorial.org/NMEICT-Intro |
| 07.53 | This is Anuradha Amrutkar from IIT Bombay signing off. |
| 07.57 | Thank you for joining Good Bye. |
