I want to solve the following problem, the cvx gives me the solution, but this solution doesn’t satisfy the constraint ( w_tm’Vw_tm <= (1+tol)^2* var_mini)？
in the main function, the called function give me the var_mini like this,
but the optimal solution w_tm doesn’t satisfy the constraint
I don’t know why ,really thanks for your help!
When optimality is claimed, the solvers called by CVX are only “guaranteed” to provide solutions which satisfy constraints to within a feasibility tolerance, which might typically be approximately 1e-8. If the constraint is violated by 1e-9, that is considered acceptable; but if that occurred in the constraint you claim is violated, it would produce logical 0 in your constraint satisfaction assessment. You should subtract one side of the inequality constraint from the other and look at the numerical value.
If you need a constraint to be strictly satisfied, even though the solver might violate it by a small amount, you need to include a buffer amount. Pick a small_positive _number, such as 1e-6; change LHS <= RHS
into LHS + small_positive_number <= RHS.
Then if CVX/solver claim the problem is solved to optimality, it is actually the case that LHS <= RHS.
General advice for the future:
Don’t use quiet until you are sure everything is working correctly. That way, you will see the solver and CVX output.
Don’t post images of your code and input data. Instead, copy and paste the actual text of code into your post and use the Prefomatted text icon. That enables forum readers to copy and paste your code into their own MATLAB session.
