In this paper we present a second order PVT (parallel variable transformation) algorithm converging to second order stationary points for minimizing smooth functions, based on the first order PVT algorithm due to Fukushima (1998). The corresponding stopping criterion, descent condition and descent step for the second order PVT algorithm are given.
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Li-Ping Pang is an lecturer in Department of Applied Mathematics, Dalian University of Technology (DUT), Dalian, China. She received her M. Sc from Polytechnic University of Jilin, Changchun, in 1992. Her research areas are (smooth, nonsmooth, discrete and numerical) optimization and applications (in science and engineering), OR methods and applications.
Zun-Quan Xia is a professor in Department of Applied Mathematics, DUT, Dalian, China. He graduated from Fudan University, Shanghai, as a graduate student in 1968. His research areas are (smooth, nonsmooth, discrete and numerical) optimization, OR methods and applications.
Li-Wei Zhang is a professor in Department of Applied Mathematics, DUT, Dalian, China. He received his M. Sc from DUT, Dalian in 1992 and Ph.D from the same university in 1998 and worked for Post-Doctorial Program in the Chinese Academy for two years. He is a visiting professor in the School of Computer Engineering, Nayang Technological University, Singapore. His research areas are (smooth, nonsmooth, discrete and numerical) optimization, OR methods and applications.
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Pang, L., Xia, Z. & Zhang, L. On a second order parallel variable transformation approach. JAMC 11, 201–213 (2003). https://doi.org/10.1007/BF02935732
AMS Mathematics Subject Classification
Key words and phrases
- Parallel algorithm
- unconstrained optimization
- second order stationary point
- linear convergence