How can i do optimization in matlab?

Hi,

I have an equation given below

y = x- at

'x' and 't' are known value. I also have field value 'z'that is known.

I want to find the value of 'a' in the equation such that error between obtained 'y' and field value 'z' is minimum.

How can i do this in matlab? I am not sure of which optimization technique in matlab can be used.

Thanks, Menaka

[Azzi Abdelmalek]

What are sizes of a and t?

[Azzi Abdelmalek]

What is field z? It does not appear in your equation

[Meenu]

Hi friend ,

sorry I was wrong before. I have changed the question now.

x and z are 1D array of ten points. a and t are single value.

Thanks

[Meenu]

'z' is the field values measured. 'x' is the value obtained using my model.

I need to find 'y' values using 'x', but the obtained 'y' should have minimum error when compared with z values.

I want to find the values

[José-Luis]

'z' is nowhere to be found in your equation.

[Meenu]

z is the array of reference values. I want to find y values using x values using the equation. I want an optimal value for 'a' so that RMSE between obtained values y and reference values z should be minimum. z is the reference value. it is not included in the equation.

Answer 1

[José-Luis]

Are you sure you asked the right question? If so, what you are asking is:

 y-x = at; %Find a and t

Since y and x are known, this can be written as

 some_value = at;

This has an infinite number of solutions, or none at all if a or t are equal to zero and some_value is not. Just pick whatever value for a and calculate t. Or vice-versa.

If what you mean was a linear regression then:

 coeff = polyfit(x,y,1);

[Meenu]

my question was wrong before friend.I have changed the question.

Answer 2

[Alan Weiss]

Let me try to guess what you are doing. You have a bunch of input data you call x, and a bunch of output data you call z. There is a scalar 'a' and another piece of input data t so that, approximately, for each index i,

 z(i) = x(i) - a*t(i)

You want to find the value of 'a' that makes this equation as true as possible, such as minimizing the sum of the squared differences.

If I am correct, write your equation as

 a*t = z - x,

where t, z, and x are column vectors. The solution is

 a = (z-x)\t

For more information, see the documentation.

Alan Weiss

MATLAB mathematical toolbox documentation

[Meenu]

the equation should be

y(i) = x(i) - a*i or y(t) = x(t) - a*t

where i= 1,2,3,.....

I have a bunch of input data you call x, and a bunch of reference data z. I want to find y as the output for each x using abouve equation. I need to find optimal value for 'a' such that RMSE between resulting y and z values should be minimum.

I can do this in MS.excel using solver. but I need to implement this in matlab.