Steepest Ascent Method to find maximum

Syed Abdul Rafay

2022 12 13

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I am looking for a problem in my implementation for steepest ascent method. My answer is in a long equation form with h in it. But I am calculating h in the loop still ther is no value of it for the answer. The solution is at the end of the function

function STPAscent(x,theta,TC)

x0 =1500;

theta0=pi/6;

i=0;

i_max=100;

ea=5;

es=1;

while (es<double(subs(ea)) && i<i_max)

fx = tan(theta0)/(2*100^2*(cos(theta0))^2) + (2*9.81*x0)/(2*100^2*(cos(theta0))^2); % derivative wrt "x"

ftheta= x0*(sin(theta0)*(100*sin(theta0)+981*x0*cos(theta0))+50)/(1000000*(cos(theta0))^4); % derivative wrt "theta"

syms h

x=x0+fx*h;

theta=theta0+ftheta*h;

f= 1000 + (x*tan(theta))/(2*100^2*(cos(theta))^2) + (9.81*x^2)/(2*100^2*(cos(theta))^2);

c=diff(f,h);

assume(h,'clear')

h=solve(c==0,h,'PrincipalValue',true);

x_new=x+fx*h;

theta_new=theta0+ftheta*h;

ea=abs((x_new-x0)/x_new)*100;

x0=x_new;

theta0=theta_new;

i=i+1;

end

fxtheta = 1000 + (x0*tan(theta0))/(2*100^2*(cos(theta0))^2) + (9.81*x0^2)/(2*100^2*(cos(theta0))^2)

simplify(fxtheta)

end

Command Window

Warning: Unable to solve symbolically. Returning a numeric

solution using vpasolve.

> In sym/solve (line 304)

In STPAscent (line 18)

fxtheta =

(981*((8836235812531391*h)/4503599627370496 + 1499.9993954193889930311396801317)^2)/(2000000*cos(pi/6 - 0.52363352427033321420523588398365)^2) + (tan(pi/6 - 0.52363352427033321420523588398365)*((8836235812531391*h)/4503599627370496 + 1499.9993954193889930311396801317))/(20000*cos(pi/6 - 0.52363352427033321420523588398365)^2) + 1000

ans =

0.0018882263675909642813601409431637*h^2 + 2.8871384744661982638760370739896*h + 2103.6241090862540686603690416302

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Syed Abdul Rafay 2022-12-13

But h is unknown and if I don't use symbolic function the code doeasn't proceed with error unrecognized variable 'h'. I have to use the h value calculate in x new to get a updated value of x .