環境系統最佳化與網流分析

課程概述
The course addresses optimization and network flows. Both the general theory and characteristics of these optimization problems as well as effective solution algorithms are presented. The course is organized into three parts: linear programming, network flows, and nonlinear programming. The linear programming part consists of simplex methods, optimality conditions, and duality. The part on network flows deals with minimal cost, transportation, assignment, maximal flow, shortest path, and multicommodity flow problems. Nonlinear programming part discusses unconstrained optimization, and penalty and barrier functions.

課程目標
(1) Linear algebra, convex analysis, polyhedral sets, and the simplex methods (2) Optimality conditions (3) Duality and sensitivity analysis (4) Minimal cost network flows (5) The transportation and assignment problems (6) Maximal flow, shortest path, multicommodity flow (7) Unconstrained optimization (8) Penalty and barrier functions

參考書目
(1) Linear Programming and Network Flows/ Mokhtar S. Bazaraa, John J. Jarvis, Hanif D. Sherali (2) Nonlinear Programming: Theory and Algorithms/ Mokhtar S. Bazaraa, Hanif D. Sherali, C. M. Shetty (3) Optimization in Operations Research/ Ronald L. Rardin

調整方式	說明
其他	由師生雙方議定

課程進度

9/05第 1 週	9/05	Introduction
9/12第 2 週	9/12	Linear algebra, convex analysis, polyhedral sets, and the simplex methods (I)
9/19第 3 週	9/19	Linear algebra, convex analysis, polyhedral sets, and the simplex methods (II) [** Presentation: 3.7 Simplex method]
9/26第 4 週	9/26	Optimality conditions [** Presentation: 5.4 The KKT optimality conditions]
10/03第 5 週	10/03	Duality and sensitivity analysis [** Presentation: 6.2 Primal-dual relationships]
10/10第 6 週	10/10	** National Holiday (No class)
10/17第 7 週	10/17	Dual simplex method [** Presentation: 6.5 Dual simplex method] [PuLP: https://coin-or.github.io/pulp/CaseStudies/a_blending_problem.html]
10/24第 8 週	10/24	** Midterm
10/31第 9 週	10/31	** No class
11/07第 10 週	11/07	** No class (Final Project proposal submission)
11/14第 11 週	11/14	Minimal cost network flows [** Presentation: 9.5 Simplex method for network flow problems]
11/21第 12 週	11/21	The transportation and assignment problems [** Presentation: Python PuLP solver]
11/28第 13 週	11/28	Maximal flow, shortest path, multicommodity flow [** Presentation: 12.2 Shortest path problem]
12/05第 14 週	12/05	Unconstrained optimization, Penalty and barrier functions [ Presentation: 16.6 Newton's method], [ Presentation: 17.5 Penalty and barrier methods], [** Presentation: 9.3 Total Unimodular]
12/12第 15 週	12/12	** Final projection presentation
12/19第 16 週	12/19	** Final projection presentation

星期四	14:00 - 17:00
*此 Office Hour 需要提前預約