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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: FTIMNLPNCPODE
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:146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.

    Contents List of Tables .......................................... 3 List of Figures ......................................... 4 1 Motivation and Introduction ......................... 10 1.1 Motivation .......................................... 10 1.2 Introduction ........................................ 12 2 Preliminaries ....................................... 17 2.1 Original time-like function ......................... 17 2.2 The Lorentz group SO0(n,1) and the Lie algebra so(n,1) ......................................................... 18 2.3 Performance profile .................................. 19 3 ODE reformulation ................................... 20 3.1 Transformation into an ODEs system .................. 20 3.2 GPS for differential equations system ................ 22 3.2.1 Group preserving scheme ........................... 23 3.2.2 One-step GPS ...................................... 26 4 Numerical experiments ............................... 28 4.1 Example 1 ........................................... 29 4.2 Example 2 ........................................... 42 4.3 Example 3 ........................................... 48 5 Conclusions ........................................... 54 Bibliography ........................................... 55

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