Scilab/C4/Optimization-Using-Karmarkar-Functions/English-timed

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.

Contributors and Content Editors

Gaurav, PoojaMoolya, Sandhya.np14