Question

6.5 A simple example of an optimization method is the random search method. This method repeatedly evaluates the function at randomly selected values of the optimization variables. If a sufficient number of samples are conducted, the optimum would eventually be found. Consider the optimization problem min f(x,y) = -8x + x2 +12y + 4y2 – 2xy x,y a. Write down the step-to-step algorithm you would use to solve the problem. b. Implement your algorithm in MATLAB to solve the problem. c. Plot the function versus the optimization variables.

Answer 1

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Answer: Given Equation : min (x,y) = -88 +2²+12y + 4y - ang xy a) Step by step solving of algorithm Let us take the initial values of x and you 'l' If f(x,y) =f(xmin, yonin, then a minar, y min=y Repeat the above step till iono literation xmin,ymin ge the optimized parameter » please take all the above steps to solve the algorithm. b) MATLAB code: cle clear t-@ (x,y)-8*x+2. Matlaky + xy . ^2 - 2ta ty, counter =0;

While counter 21016) hed x=2* randn()+si y = 2* sandn()-1; amin= 1; throple ymin = 1; if f(x,y) = f(xmin, yonin) xminds can uses (2 x 20 yuinzy; na povodotogel end counter a counter t sine rims End to avode displa min, malkirolo displynin); e) plotting: - % ploting figure (1) kelte 1023-4:01:10]; yalis [-4;0.1.5];

[xx,yy] =meshgrid (xaris, yanis); sorf (xx,yy, f (xx,yy)); xlable("xaxis"); ylable("yaris"); zlable ("function"); Execute the above code and you will get the output. 250 200 Function. 59 6. 5 10 ganie n-anis