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A Study on Efficient Algorithms for some Numerical Optimization Problems
DC Field | Value | Language |
---|---|---|
dc.contributor.advisor | 신동우 | - |
dc.contributor.author | 이선정 | - |
dc.date.accessioned | 2017-07-14T00:40:09Z | - |
dc.date.available | 2017-07-14T00:40:09Z | - |
dc.date.issued | 2013-02 | - |
dc.identifier.other | 000000010501 | - |
dc.identifier.uri | https://hdl.handle.net/10371/121264 | - |
dc.description | 학위논문 (박사)-- 서울대학교 대학원 : 수리과학부, 2013. 2. 신동우. | - |
dc.description.abstract | This thesis is mainly divided into two parts: parameter estimation problem in linear differential equations and a minimization algorithm which is applicable to some industrial problem.
In general, mathematical optimization problems are to find optimal ele- ments of a set which minimize (or maximize) the value of a given objective function. It is well known problem and arises in a various field of applications such as science, engineering, business and so on. It has a long history and there are still very much a work in progress. Optimization problems usually depend on the properties of objective func- tions involved. If functions are simple, e.g., linear, the the problem is easy to solve and moreover mathematical theories completed. If it is complex, however, it is hard to solve it theoretically and/or numerically. In this thesis, we suggest algorithms which is related to two specific opti- mization problems. These problems are both include nonlinear objective func- tions. The first part is to find a optimal parameter function of a differential equation and the second part is to find optimal solution of a facility location problem. Each parts contains theories about the solution, such as the exis- tence and the uniqueness of the optimal solution, and numerical examples are included. | - |
dc.description.tableofcontents | Abstract i
I Parameter Estimation Problem 1 Chapter 1 Introduction 2 1.1 Background............................. 2 1.2 Motivation ............................. 3 1.3 Model problem ........................... 4 Chapter 2 Basic Properties of Algorithm 8 2.1 CaseStudy ............................. 8 2.1.1 The case where the subintervals are known . . . . . . . 8 2.1.2 The case where the subintervals are yet to be determined 13 2.2 An algorithm for parameter function estimation . . . . . . . . . 22 Chapter 3 Numerical Simulations 27 3.1 Data set 1.............................. 27 3.2 Data set 2.............................. 30 3.3 Details of calculation in Lemma 2.1.6. . . . . . . . . . . . . . . 33 II Facility Location Problem 39 Chapter 4 Introduction 40 Chapter 5 The nonlinear minimax problem 44 5.1 Reformulation of the minimax problem. . . . . . . . . . . . . . 44 5.1.1 Algorithm for the location of a circle . . . . . . . . . . . 51 5.1.2 Computational complexity................. 51 Chapter 6 Numerical results 53 6.1 Test case 1 ............................. 53 6.2 Test case 2 ............................. 54 6.3 Test case 3 ............................. 58 6.4 Conclusions............................. 58 국문초록 63 | - |
dc.format | application/pdf | - |
dc.format.extent | 1205730 bytes | - |
dc.format.medium | application/pdf | - |
dc.language.iso | en | - |
dc.publisher | 서울대학교 대학원 | - |
dc.subject.ddc | 510 | - |
dc.title | A Study on Efficient Algorithms for some Numerical Optimization Problems | - |
dc.type | Thesis | - |
dc.description.degree | Doctor | - |
dc.citation.pages | 63 | - |
dc.contributor.affiliation | 자연과학대학 수리과학부 | - |
dc.date.awarded | 2013-02 | - |
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