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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/23037完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 王偉仲(Weichung Wang) | |
| dc.contributor.author | Yu-Ting Lin | en |
| dc.contributor.author | 林雨亭 | zh_TW |
| dc.date.accessioned | 2021-06-08T04:38:51Z | - |
| dc.date.copyright | 2009-08-19 | |
| dc.date.issued | 2009 | |
| dc.date.submitted | 2009-08-15 | |
| dc.identifier.citation | [1] J. F. Cai, R. Chan, L. Shen, and Z. Shen. Convergence analysis of tight framelet approach for missing data recovery. Advanced in Computational Mathematics, Springer Netherlands, 2008.
[2] J. F. Cai, R. Chan, and Z. Shen. A framelet-based image inpainting algorithm. Appl. Comput. Harmon. Anal., 23:1112-1120, 2007. [3] R. B. Chan and W. Wang. Finding effective points by surrogate models with overcomplete bases. Journal of Computational and Applied Mathematics, 217(1):110-122, 2008. [4] W. Cheney and D. Kincaid. Numerical Mathematics and Computing. Brooks/Cole, fifth edition, 2004. [5] Gregory E. Fasshauer. Meshfree Approximation Methods with MARLAB, volume 6 of Interdisciplinary Mathematical Sciences. World Scientific, 2007. [6] H. M. Gutmann. A radial basis function method for global optimization. Jourmal of Global Optimization, (19):201-227, 2001. [7] Atkinson Han. Elementary Numerical Analysis. John Wiley and Sons, Inc., third edition, 2004. [8] L. C. Lai. Adaptive search regions in derivative free optimization problems. Master’s theses, National University of Kaohsiung, 2008. [9] J. Sacks, W. J. Welch, T. J. Mitchell, and H. P. Wynn. Design and analysis of computer experiments. Statistical Science, 4(4):409-423, 1989. [10] Virginia Torczon. On the convergence of pattern search algorithms. SIAM Journal on Optimization, 7(1):1-25, February 1997. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/23037 | - |
| dc.description.abstract | 如何找出連續函數的極値是本論文所探討的最佳化問題。首先，針對自適區域調整演算法其收斂性證明不完整的部分予以補足。再來，提出新的演算法，結合影像處理和最佳化領域，將影像處理應用於最佳化問題，而經由此種方式所建構出的替代平面，與目標函數圖形具有高度的相似性，並可反映出函數圖形的主要特徵。最後，提出估計最小點位置的充分條件；亦即，經由一系列點收斂至目標函數圖形的替代平面，則目標函數的極値點將可被估計出。 | zh_TW |
| dc.description.abstract | This paper investigates a method for solving optimization problems
to find the minimizers of a function. To this end, the algorithm derived from image process generates a surrogate surface to pick initial points and then estimates the minimizers. Results indicated that the surrogate surface is similar to the real one. The minimal points can be correctly estimated in diversified cases. The algorithm is adaptive on constructing a surrogate surface preserving the main feature of the real one. Moreover, this paper gives complete convergence analysis on the Adoptive Search Regions Method and states that the minimizer of a function can be estimated by specific surrogate surfaces. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-08T04:38:51Z (GMT). No. of bitstreams: 1 ntu-98-R96221012-1.pdf: 1560040 bytes, checksum: 358f65548c7e70709194c1168b9d2a53 (MD5) Previous issue date: 2009 | en |
| dc.description.tableofcontents | Contents
口試委員會審定書i 誌謝 ii 中文摘要 iii 英文摘要 iv 1 Introduction 1 2 Optimization Problem 2 3 Surrogate Assisted Algorithms 3 3.1 The Adaptive Search Regions Method 3 3.1.1 Main Components of The Algorithm 4 3.1.2 Multiple Minima 9 3.1.3 Comparison Between the ASRM and the Pattern Search Method 10 3.1.4 The Algorithm 11 3.2 The Framelet-based Method 13 3.2.1 Notations 14 3.2.2 Framelets in L_2(R) 14 3.2.3 Frames in R^N 15 3.2.4 Framelet-based Inpainting Algorithm 17 3.3 Global Method 19 4 Convergence Analysis 20 4.1 The Adaptive Search Regions Method 20 4.1.1 The Step Structure 20 4.1.2 The Limit of The Step Control Parameter 23 4.1.3 Global Convergence 24 4.1.4 The Stronger Result 30 4.1.5 Global Minimal Point Searching 33 4.2 The Framelet-based Method 35 4.2.1 Numerical Experiments 36 4.2.2 Theoretical Results 38 4.3 Global Method 40 4.3.1 Convergence Analysis 41 4.3.2 Pointwise Convergence of Surrogate to Objective Function 49 4.3.3 Native Spaces for Strictly Positive Definite Functions 52 4.3.4 Error Bounds 54 5 Conclusion 56 Reference 60 List of Figures 1 The graphs of true functions and the surrogate surfaces 58 2 The iteration number vs. the error between the true function graph and the surrogate 59 | |
| dc.language.iso | en | |
| dc.subject | 收斂分析 | zh_TW |
| dc.subject | 無微分 | zh_TW |
| dc.subject | 最佳化 | zh_TW |
| dc.subject | 點收斂 | zh_TW |
| dc.subject | 影像填補 | zh_TW |
| dc.subject | 自適區域調整演算法 | zh_TW |
| dc.subject | 替代平面 | zh_TW |
| dc.subject | optimization | en |
| dc.subject | pointwise converge | en |
| dc.subject | image inpainting | en |
| dc.subject | Framelet | en |
| dc.subject | ASRM | en |
| dc.subject | convergence analysis | en |
| dc.subject | surrogate | en |
| dc.subject | derivative-free | en |
| dc.title | 以替代平面輔助之無微分最佳化演算法的收斂分析 | zh_TW |
| dc.title | Analysis and Development of Surrogate Assisted Derivative-free Optimization Algorithms | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 97-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 陳瑞彬,王振男 | |
| dc.subject.keyword | 最佳化,無微分,替代平面,收斂分析,自適區域調整演算法,影像填補,點收斂, | zh_TW |
| dc.subject.keyword | optimization,derivative-free,surrogate,convergence analysis,ASRM,Framelet,image inpainting,pointwise converge, | en |
| dc.relation.page | 61 | |
| dc.rights.note | 未授權 | |
| dc.date.accepted | 2009-08-17 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| 顯示於系所單位： | 數學系 | |
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