凸優化應用於許多領域，像是自動控制系統，信號處理，通訊與網路，電子電路設計，數據分析與建模，統計學，及金融等等。
在近來運算能力提高與最優化理論發展下，一般的凸優化已經接近簡單的線性規劃。
本論文的理論部分主要依據[1]。本論文將先介紹線性規劃下的原始對偶不可行內點算法[1]，再比照[1]的算法，給出線性約束下凸規劃的原始對偶不可行內點算法，並證明算法有全局收斂性

Convex minimization has applications in a wide range of disciplines, such as
automatic control systems, estimation and signal processing, communications and net-
works, electronic circuit design, data analysis and modeling, statistics (optimal design),
and nance. With recent improvements in computing and in optimization theory, con-
vex minimization is nearly as straightforward as linear programming. The theoretical
part of this thesis follow the work in [1]. This paper rst introduces the primal-dual
infeasible interior point algorithm for linear programming[1], then uses the model of
the algorithm in [1] to obtain the primal-dual infeasible interior point algorithm for
linearly constrained convex programming, and the algorithm has global convergence.

Contents
Chapter1 Introduction 1
1.1 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 A primal-dual infeasible-interior-point algorithm for linear programming 6
1.2.1 Linear programming . . . . . . . . . . . . . . . . . . . . . . . . 6
1.2.2 Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Chapter2 An Infeasible Interior Point Algorithm for Linearly Constrained Con-
vex Programming 13
2.1 Linearly constrained convex programming . . . . . . . . . . . . . . . . 13
2.2 Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3 Global convergence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

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