Difference between revisions of "Scilab/C4/Optimization-Using-Karmarkar-Functions/English-timed"
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| 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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| − | | | + | |what is meant by '''Optimization?''' |
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|00:15 | |00:15 | ||
| − | | | + | |and How to use Scilab function '''karmarkar''' for optimization. |
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|00:22 | |00:22 | ||
| − | | | + | |minimize or maximize a given '''objective function''' |
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| 00:26 | | 00:26 | ||
| − | | | + | |which is also called as '''Cost function''' sometimes, |
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| 00:30 | | 00:30 | ||
| − | | | + | | by varying the decision variables. |
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|00:33 | |00:33 | ||
| − | |The decision variables are varied subject to the | + | |The decision variables are varied subject to the predefined constraints. |
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| 00:44 | | 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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|00:58 | |00:58 | ||
| − | |The Scilab function Karmarkar is used for | + | |The Scilab function '''Karmarkar''' is used for |
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|01:01 | |01:01 | ||
| − | | | + | |optimizing the linear objective function, |
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|subject to linear constraints | |subject to linear constraints | ||
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| 01:07 | | 01:07 | ||
| − | ||on the decision variables | + | ||on the decision variables. |
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|01:10 | |01:10 | ||
| − | || We will solve the following example using ''' | + | || We will solve the following example using '''Karmarkar''' function: |
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| 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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|''' '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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||'''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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|01:36 | |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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| 01:42 | | 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 | |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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||You can see the calling sequence of the argument. | ||You can see the calling sequence of the argument. | ||
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| 02:03 | | 02:03 | ||
| − | |The argument | + | |The argument explanation, description and some examples in the '''help browser.''' |
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|02:12 | |02:12 | ||
| − | | Close the ''' | + | | Close the '''Help Browser '''. |
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|02:14 | |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 | | 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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| 02:25 | | 02:25 | ||
|''' 'x' opt:''' is the optimum solution . | |''' 'x' opt:''' is the optimum solution . | ||
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| 02:28 | | 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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|02:46 | |02:46 | ||
| − | |''' 'y' opt''' : is the structure containing the dual solution | + | |''' 'y' opt''' : is the structure containing the dual solution. |
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|This gives the Lagrange multipliers. | |This gives the Lagrange multipliers. | ||
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| 02:53 | | 02:53 | ||
| − | ||Input arguments are ''' 'Aeq' 'beq ' | + | ||Input arguments are ''' 'Aeq' 'beq' 'c' 'x' zero 'rtolf 'gam' 'maxiter' 'outfun' 'A' 'b' 'lb' and 'ub' ''' |
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|| ''' 'Aeq' ''' : is the Matrix in the linear equality constraints. | || ''' 'Aeq' ''' : is the Matrix in the linear equality constraints. | ||
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| ''' '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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|''' 'c' ''' : is the '''Linear objective function''' co-efficients of ''' 'x'. ''' | |''' 'c' ''' : is the '''Linear objective function''' co-efficients of ''' 'x'. ''' | ||
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||''' 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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|''' '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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|''' 'outfun' ''' : is the additional user-defined output functions . | |''' 'outfun' ''' : is the additional user-defined output functions . | ||
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||''' 'lb' ''': is the ''' lowerbound''' of ''' 'x'.''' | ||''' 'lb' ''': is the ''' lowerbound''' of ''' 'x'.''' | ||
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| − | |Go to the ''' scilab console | + | |Go to the ''' scilab console''' and type: |
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|'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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|04:26 | |04:26 | ||
| − | |And press Enter | + | |And press Enter. |
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|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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| − | | And press '''Enter''' | + | | And press '''Enter'''. |
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| − | |And press ''' Enter''' | + | |And press ''' Enter'''. |
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| − | |And press '''Enter''' | + | |And press '''Enter'''. |
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| − | |Now clear the '''Scilab console using clc | + | |Now clear the '''Scilab console''' using '''clc''' command. |
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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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| − | | And Press ''' | + | | And Press '''Enter'''. |
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| − | | Press Enter to continue the Display | + | | Press Enter to continue the Display. |
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| 06:14 | | 06:14 | ||
| − | | This will give the output as shown on the screen | + | | This will give the output as shown on the screen |
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| 06:18 | | 06:18 | ||
| − | | | + | | where '''xopt''' is the ''' optimal solution''' to the problem, |
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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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| 06:39 | | 06:39 | ||
| − | |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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| 06:46 | | 06:46 | ||
| − | | | + | |in which they have been listed above, while calling the function. |
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| 06:51 | | 06:51 | ||
| − | |In this tutorial, we learned | + | |In this tutorial, we learned: |
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| − | |Use of Scilab function | + | |Use of Scilab function '''Karmarkar''' in optimization to solve linear problems. |
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| 07:01 | | 07:01 | ||
| − | |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 | |07:08 | ||
| − | | Watch the video available at the following link | + | | Watch the video available at the following link. |
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| − | | It summarises the Spoken Tutorial project | + | | It summarises the Spoken Tutorial project. |
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| − | ||The spoken tutorial project Team | + | ||The spoken tutorial project Team: |
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||Conducts workshops using spoken tutorials | ||Conducts workshops using spoken tutorials | ||
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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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|07:27 | |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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| − | |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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| − | |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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| − | |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 15:29, 2 March 2015
| 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 predefined 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 explanation, 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 |
| 07:08 | Watch the video available at the following link. |
| 07:10 | It summarises the Spoken Tutorial project. |
| 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 |
| 07:23 | Gives certificates to those who pass an online test. |
| 07:27 | For more details, please write to contact@spoken-tutorial.org. |
| 07:34 | Spoken Tutorial Project is a part of the Talk to a Teacher project. |
| 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. |
