Scilab/C4/Optimization-Using-Karmarkar-Functions/English-timed
From Script | Spoken-Tutorial
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 |
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07:53 | This is Anuradha Amrutkar from IIT Bombay, signing off. |
07:57 | Thank you for joining. Good Bye. |