The author proposes an enumeration sequential quadratic programming algorithm to solve convex bilevel programming problems in an optimistic approach. The upper and lower level objective functions are convex and the feasible region is a polyhedron. From monotonicity principles a new concept of monotonicity networks is introduced. A monotonicity path is used to express the tightness of some subsets of the primal and dual lower level constraints, depending on the current rational solution. At each step of the algorithm, monotonicity paths are used to compute an improving rational solution within the tightness of primal-dual lower level constraints. Given a feasible or rational solution in a branch and bound framework, the method performs a sequential investigation on some indexes of lower level primal-dual variables in order to compute some improved rational solutions.