Equality constraint when solving quadratic programming

[wang lingyi]

I want to solve a  quadratic programming problem(QP) which has equality and inequality constraint. The mathematical description of optimization problem is attached as below. I use yalmip and mosek solver to solve my problem. And I define my equality constraint by imposing A_{equality}x <= b_{equality},  A_{equality}x>= b_{equality}. I guess as the solver has a certain degree of robustness, it may be relaxed within some tolerance, e.g. 10^(-16). Therefore, the equality constraints are not strictly satisfied. So I wonder is there any way to impose strict equality constraint when solving a QP problem? 

Attached please find my description of optimization problem and prob structure and data output file. Thank you very much for any useful advice~

[Johan Löfberg]

obtaining feasibility with a numerical tolerance of 10^-16 is just not a realistic expectation.

the best you can do if this is a must is to explicitly solve the equalities, and then work with the reduced basis, i.e if you have x and y and x+y==1, you derive the solution x=1-y and replace in the model, or alternatively [x,y]=[0.5,0.5]+[1,-1]z, i.e. symbolically compute the nullspace H and a feasible solution and write x as Hz+x0  for a new variable z