This paper considers an explicit continuation method with the trusty time-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 one matrix-vector product, other than the traditional and representative optimization method such as the sequential quadratic programming (SQP) or the latest continuation method such as Ptctr \cite{LLS2020}, which needs to solve a quadratic programming subproblem (SQP) or a linear system of equations (Ptctr). Thus, Eptctr can save much more computational time than SQP or Ptctr. Numerical results also show that the consumed time of EPtctr is about one tenth of that of Ptctr or one fifteenth to 0.4 percent of that of SQP. Furthermore, Eptctr can save the storage space of an $(n+m) \times (n+m)$ large-scale matrix, in comparison to SQP. The required memory of Eptctr is about one fifth of that of SQP. Finally, we also give the global convergence analysis of the new method under the standard assumptions.
翻译:本文考虑一种明确的延续方法,即信任的时步制和用于线性限制优化问题的有限模拟 BFGS (L-BFGS) 更新公式(Eptctr) 。 在每次迭代中, Eptctr 仅涉及矢量和一矩阵矢量产品内部产品三对配方,而传统和代表性优化方法,如连续四级编程(SQP)或Ptctr的消费时间约为Ptcr的十分之一,或SQP的百分之一至0.4%。此外, Eptr 能够将一个 $(n+P) 子问题(SQP) 或直线性方程系统(Ptctr) 。因此, Eptctr 只能节省比 SQP 或Ptcr 产品内置的三对数。 数值结果还表明, EPtctr 的消耗时间大约是Ptr的十分之一或SQPQP的百分之一至0.4%。 此外, Eptr可以将一个最大存储空间的存储空间的存储器的存储器的存储空间到S+n最后的Smlmlum 的大小分析。