Initialize the parameters: relative tolerance , , , ; 
repeat
 1. Compute the search direction as an approximate solution to the Newton system  (14) by preconditioned conjugate gradient method;  2. Compute the step size a by backtracking line search;  3. Update the iterate by ;  4. Construct a dual feasible point from (10);  5. Evaluate the duality gap from (11);  6.
quit if ;  7. Update t: where and . 
