Function optimization meeting some conditions

I have a array ht(i,j) and i want to calculate de values that minimize de sumatory of sum((hti,j)-h(j).^2), meeting the conditions: h(j)<120, h(j+1)>h(j) and h(j+1)-h(j)<1.25. I am trying doing it with the optimizetool but i don´t know how, and using fmincon i have done this:

function [h] = hp3(ht)


[n,m]=size(ht);

Ins = @(h) sum((ht - h).^2);



h0 = zeros(size(m)); 

A = [];
b = [];
Aeq = [];
beq = [];
lb = [];
ub = [];


h = fmincon(Ins, h0, A, b, Aeq, beq, lb, ub, @constraints);

end

function [c, ceq] = constraints(h)
    c = h(2:end) - h(1:end-1);
    ceq = [];
end

[Jon]

Also your line of code:

h0 = zeros(size(m));

Doesn't look correct, m is a scalar so size(m) will by 1,1

I think you want

h0 = zeros(m,1);

Answer 1

[Jon]

In your case, you only have linear constraints, and bound constraints. So you don't need to use a function to define non-linear constraints.

You can assign your linear constraints ("h(j+1)>h(j) and h(j+1)-h(j)<1.25") as, here I write it for h with only 5 elements as an example (If they are large you could define the matrices below using, for example the diag function, I wrote them out explicitly here so you could easily see what they look like):

% h(j) - h(j+1) <= 0
A1 = [1 -1 0 0 0 ;
     0  1 -1 0  0;
     0  0  1 -1 0;
     0  0  1 -1 0;
     0  0  0  1 -1]
b1 = [0;0;0;0;0]
% h(j+1) - h(j) <= 1.25
A2 = [-1 1 0 0 0;
       0 -1 1 0 0;
       0  0 -1 1 0;
       0  0  0 -1 1]
b2 = [1.25;1.25;1.25;1.25;1.25];

% Combine into overall constraint
A = [A1;A2];
b = [b1;b2];

Assign bound constraints (" h(j)<120"

% Bound constraints
lb = -inf
ub = 120

No equality constraints

Aeq = [];
beq = [];

% Call optimization

h = fmincon(Ins, h0, A, b, Aeq, beq, lb, ub);