# 臺灣博碩士論文加值系統

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 在這篇文章中, 我們首先介紹預言者-修正者內點法, 並依據 這個方法做一些變形. 接著, 我們透過數值的實驗來觀察這些變形之間的差異. 最後, 再針對這些差異做出幾點結論.
 In chapter 2 of this paper, we will introduce the basic ideas of the interior point algorithms. Consider the problems we would like to solve, and propose how to solve it based on the logarithmic barrier function approach. Then compute some kinds of the search directions and choose the step lengths. Introduce an feasible interior-point algorithm, and its iteration complexity. The last part of chapter 2, we would like to find a suitable parameter for the algorithm by Klee-Minty problems. Then in chapter 3, write down some variate algorithms we used, explain their characteristics and how to complete the computer programs (By FORTRAN 77) for them. Chapter 4 is numerical experiments and conclusions. The first section is about the experiment results for all algorithms. We will record the iteration numbers and CPU time of them. Then is the conclusions.
 1. Introduction 2 1.1 History} 1.2 What we want to do 2. Basic ideas of interior point methods 6 2.1 Introduction to IPMs 2.2 A predictor-corrector feasible interior-point algorithm 2.3 Complexity analysis of algorithm 1 2.4 Numerical experiment for algorithm 1 3. Variations of the interior-point algorithms 19 3.1 Change the search directions of algorithm 1 3.2 An infeasible-starting feasible interior-point algorithm 4. Numerical experiments and conclusions 24 4.1 Numerical results of these algorithms 4.2 Conclusions
 [1] Adler, I., Karmarkar, N., Resende, M. G. C. and Veiga, G. (1989) "An implementation of Karmarkar's algorithm for linear programming", Mathematical Programming, 44, 297-335.[2] Fang, S. C. and Puthenpura, S., Linear Optimization and Extensions: Theory and Algorithms, Prentice-HillInternational, Inc. (1993).[3] Hertog, den D., Interior Point Approach to Linear, Quadratic and Convex Programming Algorithms and Complexity.KLUWER ACADEMIC PUBLISHERS. (1994).[4] Megiddo, N. and Shub, M. (1989) "Boundary behavior of interior point algorithms in linear programming",Mathematicsof Operations Research, 14, 97-146.[5] Mizuno, S., Todd, M.J. and Ye, Y., (1990) "On adaptive-step primal-dual interior-point algorithm for linear programming",Technical Report No. 944, School of Operations Researchand Industrial Engineering, Cornell University, Ithaca, NY,Mathematics of Operations Research 18, (1993), 964-981.[6] Mizuno, S., Megiddo, N. and Kojima, M., "A primal-dual infeasible interior-point algorithm for linear programming,"Mathematical Programming 61, (1993), 263-280.[7] Mizuno, S., "Polynomiality of infeasible-interior-pointalgorithms for linear programming,"Mathematical Programming 67, (1994), 109-119.[8] Stephen G. Nash and Ariela Sofer, Linear and Nonlinear Programming, McGRAW-HILL INTERNATIONAL EDITIONS. (1996).[9] Zhao, G. Sun, J. and Zhu J. (1995), "A primal-dualaffine scaling algorithm with necessary centering as asafeguard", Optimization Vol.35, 333-343.[10] Zhao, G., "On the choice of parameters for power-series interior point algorithms in linear programming",Mathematical Programming 68 49-71, 1995.
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