This paper considers an explicit continuation method with the trustytime-stepping scheme and the limited-memory BFGS (L-BFGS) updating formula(Eptctr) for the linearly constrained optimization problem . At every iteration, Eptctr only involves three pairs of the inner product of vector and onematrix-vector product . The consumed time of EPtctr is about one tenth of thatof thatof Ptctr or one fifteenth to 0.4 percent of that of SQP. Furthermore, the storage space of an $(n+m) \times (n+ m)$ large-scale matrix, incomparison to SQP . The required memory of the new method is about a fifth of that . ofSQP. Finally,

Author(s) : Xin-long Luo, Jia-hui Lv, Hang Xiao