2021/01/18 by Xin-long Luo, Luo, Xin-long, Jia-hui Lv +3 · 1 citation
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #Dynamical Systems (math.DS) #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Numerical methods for differential equations #Optimization and Control (math.OC) #cs.NA #math.DS #math.NA #math.OC
paper · pdf · doi:10.48550/arxiv.2101.07055
arXiv admin note: substantial text overlap with arXiv:2012.14808; text overlap with arXiv:2005.05965
arxiv created 2021/01/18 · openalex publication_date 2021/01/18 · arxiv updated 2021/01/19 · openalex created_date 2021/02/01 · openalex updated_date 2026/07/28
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 \citeLLS2020, 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) × (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.