In fmincon i want to supply the Gradient of constraints. My constraints are very large and the optimization variables are also very large. I tried to use myAD and able to calculate the gradient of objective function but not of constraints

Problem is having equality constraints(ceq) as well as inequality constraints(c) of the form

for n=1:iter-1
c(n) = -y(optvar*(n)+1)+15-(T(n+1)-4)^4;  %optvar=7
end

and ceq as

for m= 1:state
        ceq(2*state*(n-1)+m)=y(optvar*n+m)-y(optvar*(n-1)+m)-(beta/gamma)*fnp1(m)*h-(1-beta/gamma)*fn(m)*h-...
            (1/2-beta/gamma)*y(optvar*(n-1)+state+alg+m)*h
end

where state,optvar are positive integer and fnp1 is some function.

How to calculate the gradient of c and ceq. As i am new to matlab so finding it difficult calculate.

Answer 1

[Matt J]

where state,optvar are positive integer and fnp1 is some function.

If optvar is the vector of unknowns, it cannot be constrained to integer values. fmincon cannot handle integer programming problems. You could try ga(). There is no gradient computation involved there.

[Divyansh]

Optvar is an integer having value 7 it is not vector only y is vector of optimization variables.....mentioned in the above code already

[Matt J]

In that case, it looks like c and ceq depend on the unknown vector y linearly. Since your constraints are linear, you should not be using the nonlcon input argument to express them. You should be using the other inputs A,b,Aeq,beq, ub,lb.

This eliminates the work completely. There are no nonlinear constraints and therefore no gradients to compute.

[Divyansh]

This was the small sample problem in which the constraint is luckily linear but the actual problem i have is having nonlinear constraints of type

c(var*n+6)=18300*sqrt(rho0)*exp(0.5*beta1(ra- y(optvar*n+1)))*y(optvar*n+4)^3.05

where rho0,beta1 are having constant value..and c depend on unknown vector y nonlinearly.

[Matt J]

This constraint looks like it is in error. Everything on the right hand side is inherently strictly positive except for y(optvar*n+4)^3.05. The constraint is therefore only satisfied at y(optvar*n+4)=0 and a discrete set of negative values, where the constraint is not differentiable.

If y(optvar*n+4)=0 is really the condition that you want, there is no need to treat y(optvar*n+4) as an unknown. Just set it to zero at the beginning and exclude it from your problem.