What is wrong with this optimization code using fmincon?

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Baisically using fmincon to solve for an unknown 2x1 matrix called A, which is optimized value for given objective function. Code error appears in 1st line below but I want A to be a 2x1. For context, x, y, and P are all vectors of the same length.
% Model section
GeRT_model = @(A) (x.*(1.-x)).*[(1.-x) x]*A;
% Parameters for experimental section below. Lots of distracting numbers.
A1 = 7.89750; B1 = 1474.08; C1 = 229.13;
A2 = 8.01195; B2 = 1698.785; C2 = 231.04;
T = 333.15;
P1sat = 10^( A1 - B1 / ((T-273.15) + C1) ) ;
P2sat = 10^( A2 - B2 / ((T-273.15) + C2) );
gamma1 = y.*P ./ (x.*P1sat);
gamma2 = (1.-y).*P ./ ( (1-x).*P2sat );
% experimental section
GeRT_exp = x.*log(gamma1) + (1.-x).*log(gamma2);
%% Optimization: Objective Function that is defined in terms of model and exp. sections. N is length of P,x,and y vectors. The rest is to set up Optimization
OBJFUN = @(A) 1/N *sum ( ( ( GeRT_model(A) .- GeRT_exp ) ./ GeRT_exp ).^2 );
% ineq constrnts
A = [];
b = [];
% eq constrnts
%[x2^2*(1-2*x1) 2*x1*x2^2; 2*x1^2*x2 x1^2*(1-2*x1)]*...
%[A12 A21]'=[log(gamma1) log(gamma2)]'
Aeq = [(1.-x).^2.*(1.-2.*x) 2.*x.*(1.-x).^2; 2.*x.^2.*(1.-x) x.^2.*(1.-2.*x)];
beq = [log(gamma1) log(gamma2)]';
lb = [];
ub = [];
A0 = [1 1]; % an initial guess for A
[A,fval] = fmincon(OBJFUN,A0,A,b,Aeq,beq,lb,ub)
Any help is much appreciated!!

Answers (1)

Walter Roberson
Walter Roberson on 23 Feb 2021
OBJFUN = @(A) 1/N *sum ( ( ( GeRT_model(A) .- GeRT_exp ) ./ GeRT_exp ).^2 );
^^
.- is not a valid operation.
A0 = [1 1]; % an initial guess for A
That is 1 x 2. That is providing an initial value for the A that is being passed into OBJFUN
OBJFUN = @(A) 1/N *sum ( ( ( GeRT_model(A) - GeRT_exp ) ./ GeRT_exp ).^2 );
OBJFUN passes it into GeRT_model
GeRT_model = @(A) (x.*(1.-x)).*[(1.-x) x]*A;
GeRT_model takes it and does matrix multiplication of something with A. With A being 1 x 2, that means the first value must be N x 1 for some N, giving an N x 2 result. But we can see several cases:
  • if x is empty, then [(1.-x) x] is empty and the * operation is invalid
  • if x is a column vector then [(1.-x) x] is N x 2 and the * operation against 1 x 2 A is invalid
  • if x is a row vector then [(1.-x) x] is 1 x (2*N) and the * operation against 1 x 2 A is invalid
so we must figure that you mean
GeRT_model = @(A) (x.*(1.-x)).*[(1.-x) x]*A.';
and that you expect x to be a column vector.
Aeq = [(1.-x).^2.*(1.-2.*x) 2.*x.*(1.-x).^2; 2.*x.^2.*(1.-x) x.^2.*(1.-2.*x)];
beq = [log(gamma1) log(gamma2)]';
Those constraints are unlikely to be satisfied. A will be a vector of two values, and Aeq*A' = beq must be true to within tolerance for all 2*N entries. Your x, y, P would have to have magic relationships with essentially no noise.

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