Scilab/C4/Optimization-Using-Karmarkar-Functions/English-timed
From Script | Spoken-Tutorial
| 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
|
| 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. |
