研究生: |
伊爾凡 Irfan Nurhidayat |
---|---|
論文名稱: |
An ordinary differential equation approach for nonlinear programming and nonlinear complementarity problem An ordinary differential equation approach for nonlinear programming and nonlinear complementarity problem |
指導教授: |
陳界山
Chen, Jein-Shan |
學位類別: |
碩士 Master |
系所名稱: |
數學系 Department of Mathematics |
論文出版年: | 2019 |
畢業學年度: | 107 |
語文別: | 英文 |
論文頁數: | 58 |
中文關鍵詞: | FTIM 、NLP 、NCP 、ODE |
英文關鍵詞: | FTIM, NLP, NCP, ODE |
DOI URL: | http://doi.org/10.6345/THE.NTNU.DM.008.2019.B01 |
論文種類: | 學術論文 |
相關次數: | 點閱:106 下載:20 |
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In this thesis, we consider an ordinary differential equation (ODE) approach for solving nonlinear programming (NLP) and nonlinear complementarity problem (NCP). The Karush-Kuhn Tucker (KKT) optimality conditions of NLP and NCP are used to get the new NCP-functions. A special technique is employed to reformulate of the NCP as the system of nonlinear algebraic equations (NAEs) later on reformulated once more by force of an original time-like function into an ordinary differential equation (ODE).
Afterwards, a group preserving scheme (GPS) is a package to reformulate an ODE into the new numerical equation in a way the ODEs system is designed into a nonlinear dynamical system (NDS) and is continued to discover the new numerical equation through activating the Lorentz group SO 0 (n, 1) and its Lie algebra so(n, 1). Lastly, the fictitious time integration method (FTIM) is utilized into this new numerical equation to determine an approximation solution in numerical experiments area.
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