Dear Adamu,

In any optimization problem first we need to define what we need to optimize: in other words we need to find one or more state variables that are part of function or set of functions that describe your system to be optimized (in your case, I suppose the problem is the design of an antenna to serve a specific scope and having a set of technical and/or economic restrictions). If this is your case, when we look at fundamental parameters describing an antenna we look at: frequency, wavelength, radiation patterns, directivity, gain, etc. They form your decision variables. The optimization function has to describe the purpose of your system (e.g. I would like my antenna to cover the transmission or reception of a signal within this power range [A, B] within this specific region, having these x, y, z technical and/or economic limitations).  Note that "parameters" is a term used for something you know or it is a given data. State variable or decision variable is the correct term for that something you need to find from the function you optimize.  Therefore, if your optimization problem is something like

minimize f(x)= a*x^3+b*x-c,

such that xMin

Thank you Very much Irina i tried the code you just gave me and it works perfectly but my main problem is how to relate it to my work or simply how to form the objective function for e.g if i want to optimize the width of my patch antenna having this formular as W=c/2f*sqrt(e+1) where c is known as 3*10^8,f is 30*10^9, and e is 4.4 so how can i formulate it in matlab

I am afraid you didn't understand your problem: the correct form of an optimization problem needs to have some sort of variable that you need to find. In your case it might be either to determine the width W of a microstrip antenna such that to have a maximum bandwidth. W of your antenna controls the input impedance of the antenna and that impedance is a physical object that can vary in a specific range. Larger widths also can increase the bandwidth. OR it might be something else that you need to minize or maximize.

In the equation you wrote, all values are known such that you perform a simple calculation, and the result of your W=3*10^8/((2*30*10^9)*sqrt(4.4+1))= ... a constant. This is not an optimization. 

You need to identify which are the values that you are allowed to vary (within some limits most probably) such that to get a maximum or a minimum width, according to your technical specifications.  

You may refer to this blog to better understand what exactly you need to maximize or minimize:

 http://www.antenna-theory.com/antennas/patches/antenna.php. 

Ok Irina please can i have your email address mine is [email protected]

I saw alot of literatures on the optimization of feeding feeding point of an antenna but i dont know how to go about it i dont know if you can guide me on that

I am into optimization of the use of antioxidants in determination of oxidative stability of vegetable oils and their methyl esters.. Wishing you the best of luck Jabire