Matlab Optimization problem, minimize a function

Hello, So I have a simple optimization problem that consists of finding a value for a variable that minimizes the difference between two other variables. For example, First input element; An Arbitrary value of X=10. Q=100; B=X*Q; C=50; The objective is to find the value of X that minimizes the difference between (X*Q) & C; f(X)=(X*Q)-C; Is there a function that will give this output or do I need to run a loop that keeps solving for X until it finds a value that minimizes the function f(X)? Thank you so much.

[Matt J]

Duplicate of post http://www.mathworks.com/matlabcentral/answers/303908-how-to-run-an-optimization-function-in-matlab-minimize-function

Answer 1

[Star Strider]

X = C/Q

[Amine Ben Ayara]

Good morning, thanks for your reply. Could it be that simple? or perhaps I did not explain correctly? So the objective is to find the value of X that minimizes the difference (X*Q)-C. Example: suppose a price P=$10.00, and Quantity Q=10, The total budget is computed B=P*Q (10*100=1000), and we have C=450, I need to find a value P* that minimizes the difference [(P*Q)-C]; with one constraint P*>0 ( price must be positive). Thank you so much

[Alan Weiss]

You did not say before that you needed a positive value of P. In that case, use lsqnonneg:

P = lsqnonneg(Q,C)

Alan Weiss

MATLAB mathematical toolbox documentation

[Star Strider]

My pleasure.

I believe it definitely could be that simple:

P = 10;                                                 % Price = $10
Q = 10;                                                 % Quantity = 10
Budget = P*Q;                                           % Total Budget
C = 450;                                                % C = ???

fcn = @(Pstar) norm(Pstar*Q - C);                       % Objective Function
Pstar1 = fminsearch(fcn, 1)                             % Determine ‘P*’

Pstar2 = C/Q                                            % Determine ‘P*’

Pstar1 =
    45

Pstar2 =
    45