Difference between revisions of "Scilab/C4/Optimization-Using-Karmarkar-Functions/English-timed"
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| − | |Dear Friends, | + | |Dear Friends, Welcome to the spoken tutorial on '''Optimization of Linear Functions with Linear Constraints Using Scilab'''. |
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|The '''Scilab function karmarkar''' is used for | |The '''Scilab function karmarkar''' is used for | ||
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|optimizing the linear objective function, | |optimizing the linear objective function, | ||
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| 01:05 | | 01:05 | ||
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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 | ||
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|| We will solve the following example using '''karmarkar''' function: | || We will solve the following example using '''karmarkar''' function: | ||
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|01:14 | |01:14 | ||
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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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|01:26 | |01:26 | ||
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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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|01:32 | |01:32 | ||
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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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|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 | ||
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||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 | |01:54 | ||
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| '''help karmarkar''' | | '''help karmarkar''' | ||
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|01:57 | |01:57 | ||
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| and press '''Enter.''' | | and press '''Enter.''' | ||
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| 01:59 | | 01:59 | ||
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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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| 02:49 | | 02:49 | ||
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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' '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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|03:09 | |03:09 | ||
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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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| 03:12 | | 03:12 | ||
| ''' 'beq' ''' :is the right hand side of the linear '''equality''' constraint. | | ''' 'beq' ''' :is the right hand side of the linear '''equality''' constraint. | ||
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| 03:17 | | 03:17 | ||
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|''' 'c' ''' : is the '''Linear objective function''' coefficients of ''' 'x'. ''' | |''' 'c' ''' : is the '''Linear objective function''' coefficients of ''' 'x'. ''' | ||
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| 03:21 | | 03:21 | ||
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| ''' 'x' zero''' : is the '''Initial guess .''' | | ''' 'x' zero''' : is the '''Initial guess .''' | ||
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|03:25 | |03:25 | ||
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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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|03:34 | |03:34 | ||
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|''' 'gam' ''' : is the Scaling factor. | |''' 'gam' ''' : is the Scaling factor. | ||
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| 03:36 | | 03:36 | ||
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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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| 03:43 | | 03:43 | ||
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|''' 'outfun' ''' : is the additional user-defined output function. | |''' 'outfun' ''' : is the additional user-defined output function. | ||
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| 03:47 | | 03:47 | ||
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| ''' 'A' ''': is the Matrix of linear inequality constraints | | ''' 'A' ''': is the Matrix of linear inequality constraints | ||
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| 03:51 | | 03:51 | ||
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| ''' '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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| 03:55 | | 03:55 | ||
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||''' 'lb' ''': is the ''' lowerbound''' of ''' 'x'.''' | ||''' 'lb' ''': is the ''' lowerbound''' of ''' 'x'.''' | ||
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| 03:58 | | 03:58 | ||
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||''' 'ub'''' are the '''upper bound''' of ''' 'x'. ''' | ||''' 'ub'''' are the '''upper bound''' of ''' 'x'. ''' | ||
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| 04:02 | | 04:02 | ||
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||Now, we can solve the given example in Scilab using '''karmarkar''' function. | ||Now, we can solve the given example in Scilab using '''karmarkar''' function. | ||
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| 04:07 | | 04:07 | ||
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|Go to the ''' scilab console''' and type: | |Go to the ''' scilab console''' and type: | ||
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| 04:11 | | 04:11 | ||
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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 | ||
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|and press Enter. | |and press Enter. | ||
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| 04:28 | | 04:28 | ||
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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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| 04:38 | | 04:38 | ||
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| and press '''Enter'''. | | and press '''Enter'''. | ||
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| 04:41 | | 04:41 | ||
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| 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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| 04:53 | | 04:53 | ||
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|and press ''' Enter'''. | |and press ''' Enter'''. | ||
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|Now clear the console using '''clc''' command. | |Now clear the console using '''clc''' command. | ||
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| 05:12 | | 05:12 | ||
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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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| 06:09 | | 06:09 | ||
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| and Press '''Enter'''. | | and Press '''Enter'''. | ||
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| 06:11 | | 06:11 | ||
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| Press Enter to continue the display. | | Press Enter to continue the display. | ||
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| 06:14 | | 06:14 | ||
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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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| 06:18 | | 06:18 | ||
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| where '''xopt''' is the ''' optimum solution''' to the problem, | | where '''xopt''' is the ''' optimum solution''' to the problem, | ||
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| 06:23 | | 06:23 | ||
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|'''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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| 06:32 | | 06:32 | ||
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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 | ||
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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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| 06:46 | | 06:46 | ||
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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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| 06:51 | | 06:51 | ||
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|In this tutorial, we learned: | |In this tutorial, we learned: | ||
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| 06:53 | | 06:53 | ||
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|What is ''' optimization?''' | |What is ''' optimization?''' | ||
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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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| 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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| It summarizes the Spoken Tutorial project. | | It summarizes the Spoken Tutorial project. | ||
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|07:14 | |07:14 | ||
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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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|07:18 | |07:18 | ||
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||The spoken tutorial project Team: | ||The spoken tutorial project Team: | ||
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|07:20 | |07:20 | ||
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||Conducts workshops using spoken tutorials. | ||Conducts workshops using spoken tutorials. | ||
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|07:23 | |07:23 | ||
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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 | ||
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||For more details, please write to contact@spoken-tutorial.org. | ||For more details, please write to contact@spoken-tutorial.org. | ||
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|07:34 | |07:34 | ||
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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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| 07:37 | | 07:37 | ||
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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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| 07:44 | | 07:44 | ||
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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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| 07:53 | | 07:53 | ||
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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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|07:57 | |07:57 | ||
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| Thank you for joining. Good Bye. | | Thank you for joining. Good Bye. | ||
Latest revision as of 11:07, 10 March 2017
| Time | Narration |
| 00:01 | Dear Friends, 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 | Output 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 constraint. |
| 03:17 | 'c' : is the Linear objective function coefficients 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 function. |
| 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 bound of 'x'. |
| 04:02 | Now, we can 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 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 optimum 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 summarizes 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. |
