Setting linear constraints for fmincon,

I am setting the linear inequality constraints for my problem in fmincon.

My problem is min_(gamma,t) t s.t -t<=0; PS(gamma) - t <= 0; - PS(gamma) - t <= 0; i want to minimize t and my optimization variables are both t and gamma. gamma is comlex in nature so i am separating real and imaginary parts for fmincon in x_opt. A and B are not correct anyone can help ?

function [A, B] = linear_constraints(x_opt---)

real_gamma = x_opt(1:Nris+2); % Real part of gamma

imag_gamma = x_opt(Nris+3:length(x_opt)-1); % Imaginary part of gamma

gamma = real_gamma + 1i * imag_gamma; % Recombine gamma as complex vector

A = zeros(0, length(x_opt));

B = zeros(0, 1);

%% Constraint (a): -t <= 0

A_a = zeros(1, length(x_opt)); % Coefficients for all variables

A_a(end) = -1; % -t in the last column

B_a = 0; % Right-hand side of constraint

% Append to A and B

A = [A; A_a];

B = [B; B_a];

%% Constraint (b): PS(gamma) - t <= 0

% PS_term is a scalar real value based on gamma

PS_term = PS(gamma);

A_b = zeros(1, length(x_opt)); % Coefficients for all variables

%A_b(1:Nris+2) = (PS_term); % Include coefficients for gamma

A_b(end) = -1; % Coefficient for -t

B_b = -PS_term; % Right-hand side of constraint

% Append to A and B

A = [A; A_b];

B = [B; B_b];

%% Constraint (d): - PS(gamma) - t <= 0

PS_term_1 = -Ps(gamma)

A_d = zeros(1, length(x_opt));

%A_d(1:Nris+2) = ; % Coefficients for gamma

A_d(end) = -1; % Coefficient for -t

B_d = (TA_PS_term); % Right-hand side of constraint

% Append to A and B

A = [A; A_d];

B = [B; B_d];

end

Answer 1

[Torsten]

If real(gamma) and imag(gamma) are vectors of optimization variables, the constraints

  PS(gamma) - t <= 0; 
- PS(gamma) - t <= 0;

are nonlinear constraints. You will have to define them in function "nonlcon".