Abstract
A modified SQP-type MFD was presented by Chen and Kostreva and its global convergence under rather mild assumptions has been proved. The numerical results showed that this modified MFD converges faster than Piron-neau — Polak’s MFD and Cawood — Kostreva’s norm-relaxed MFD. However, the rate of convergence and especially the relationship between this rate and the choice of the introduced speed-up factors have not been investigated yet. This paper studies the asymptotic rates of convergence of SQP-type MFD based on the modified MFD. Our analysis is completely focused on a direction finding subproblem (DFS) which is a QP problem like that of the modified MFD. Based on the modified MFD, we have analyzed the rate of convergence of SQP-type MFD and its bound. This paper shows that SQP-type MFD is at least linearly convergent and induced a better bound on convergence ratio than the Cawood — Kostreva’s analysis. In addition, for the case that all constraints are linear, we show that the modified MFD is superlinearly convergent under the assumptions.
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Kostreva, M.M., Chen, X. (2001). Asymptotic Rates of Convergence of SQP-Type Methods of Feasible Directions. In: Yang, X., Teo, K.L., Caccetta, L. (eds) Optimization Methods and Applications. Applied Optimization, vol 52. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3333-4_13
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DOI: https://doi.org/10.1007/978-1-4757-3333-4_13
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