Finding of arg max of a function using Gradient descent

Let F=abs(a+bx)^2

Problem: Find x to get the maximum of F.

How to proceed with graident descent to solve this problem in matlab?

[John D'Errico]

PLEASE STOP posting obvious homework assignments withg no effort made.

[Murali Krishna AG]

This is not home work assignment. It's a part of my research work. I am posting after many attempts.

Answer 1

[Sam Chak]

Hi @Murali Krishna AG

I usually plot the graph if possible before attempting to solve a particular problem.

In your case, I'm unsure if you want to find the maximum or minimum of .

a = 1;
b = 1;
F = @(x) abs(a + b*x).^2;
x = linspace(-4, 2);
plot(x, F(x)), grid on, xlabel('x'), ylabel('F(x)')

[Murali Krishna AG]

yes, I want to find the maximum of F(x)

[Sam Chak]

Alright then, @Murali Krishna AG. From the graph that I have plotted over the region above (assuming , ), there are two maximum values. Which one is desirable?

[John D'Errico]

Note that this person has posted multiple homework problems, and has never made any attempt to solve them.

[Murali Krishna AG]

Hello, I made many attempts but I couldn't get how to solve this using projected gradient descent. BTW This is not homework problem.

[Murali Krishna AG]

@Sam Chak Thanks for your answer. Can we do without assuming a,b, values?

[Sam Chak]

@Murali Krishna AG, I'm actually no good at gradient descent method. But @John D'Errico is a mathematician and he is very good at solving optimization problems. Anyhow, I was trying to show you that no matter what values a and b are, the function is a parabola that opens upwards. That's why I plotted it out in the first place for you to realize it by yourself.

Usually, if the question not a homework, we don't put it like "Let this equation be ... something. Find/Solve ... using this method."

Instead, we put it like, "I'm solving this problem (show equation) with this MATLAB code:

% Type MATLAB code here:
fplot('abs(a + b*x).^2')

Error using fplot
Input must be a function or functions of a single variable.

and the Error message is shown above."

[Murali Krishna AG]

@Sam Chak Okay. Thank you very much. I will change my way of posting the questions.