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线性规划讲课大纲 LINEAR PROGRAMMING Outline • Course objective • Pre-requisites • Course content • Grading and exams • Classroom rules • Textbook and references LECTURE 1: INTRODUCTION Outline • What is Linear Programming? • Why to study Linear programming? • How to study Linear Programming? • History of Linear Programming • How to solve an LP problem? • Where to go? LECTURE 2: PRELIMINARIES 1. Standard form LP 2. Embedded assumptions 3. Converting to standard form LECTURE 3: GEOMETRY OF LP 1. Terminologies 2. Background knowledge 3. Graphic method 4. Fundamental theorem of LP LECTURE 4: SIMPLEX METHOD 1. Simplex method 2. Phase one method 3. Big M method LECTURE 5: DUALITY AND SENSITIVITY ANALYSIS 1. Dual linear program 2. Duality theory 3. Sensitivity analysis 4. Dual simplex method LECTURE 6: INTERIOR POINT METHOD 1. Motivation 2. Basic concepts 3. Primal affine scaling algorithm 4. Dual affine scaling algorithm LECTURE 7: ROBUST LINEAR OPTIMIZATION 1. Motivation 2. Robust model 3. Solution methods

LECTURE 6: CONVERGENCE OF AN ALGORITHM 1. Concept of convergence 2. Rate of convergence LECTURE 7: CONSTRAINED OPTIMIZATION - INTRODUCTION 1. Basic terminologies 2. KKT conditions – motivation 3. Background knowledge LECTURE 8: CONSTRAINED OPTIMIZATION – OPTIMALITY CONDITIONS 1. Basic concepts 2. Necessary conditions – KKT conditions 3. Sufficient conditions LECTURE 9: CONSTRAINED OPTIMIZATION – SENSITIVITY ANALYSIS AND DUALITY 1. Basic concepts 2. Sensitivity analysis 3. Duality theory LECTURE 10: CONSTRAINED OPTIMIZATION – LAGRANGIAN DUAL PROBLEM 1. Lagrangian dual problem 2. Duality gap 3. Saddle point solution LECTURE 11: SOLUTION METHODS FOR CONSTRAINED OPTIMIZATION 1. Primal approach 2. Penalty and barrier methods 3. Dual approach 4. Primal-dual approach LECTURE 12: QUADRATICALLY CONSTRAINED QUADRATIC PROGRAMMING (QCQP) 1. Motivation 2. Convex QCQP 3. General QCQP 4. On-Going Research

台湾交通大学方述成线性规划第三讲讲义 LECTURE 2: PRELIMINARIES 1. Standard form LP 2. Embedded assumptions 3. Converting to standard form Standard form LP • Key elements: Explicit form

台湾交通大学方述成线性规划第二讲讲义 LECTURE 1: INTRODUCTION Shu-Cherng Fang North Carolina State University – Fall 2017 Outline • What is Linear Programming? • Why to study Linear programming? • How to study Linear Programming? • History of Linear Programming • How to solve an LP problem? • Where to go? What is Linear Programming (LP)? • Optimize a linear objective function of decision variables subject to a set of linear constraints. • Example

台湾交通大学方述成线性规划第一讲讲义，需要配套视频可以私聊 OR/MA/ISE 505: LINEAR PROGRAMMING A Graduate Level Course Shu-Cherng Fang North Carolina State University – Fall 2017 Outline • Course objective • Pre-requisites • Course content • Grading and exams • Classroom rules • Textbook and references

Matrix Analysis 第二週課程講義 A nn. Def. AnormalifA*AAA* A Hermitian (self-adjoint) if A*  A A0 if Ax,x 0 xn. Properties: Matrix Analysis 第二週課程講義 實變函數論─應用數學系 吳培元老師

台湾交通大学，矩阵分析讲义 非常不错。 References: (1) R.A. Horn & C.R. Johnson, Matrix Analysis, Cambridge Univ. Press, Cambridge, 1985. (2) R.A. Horn & C.R. Johnson, Topics in Matrix Analysis, Cambridge Univ. Press, Cambridge, 1991.

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