15.094J 鲁棒系统优化建模与计算

MIT Course 15 · Operations Research/Statistics · 课号 15.094J

TL;DR

• 参数不确定性下的现代鲁棒优化（Robust Optimization），将不确定集映射为可处理凸锥规划。
• 椭球不确定集导向二阶锥规划（SOCP），多面体不确定集保持线性对偶易解性。
• 半正定规划（SDP）与对偶极小极大定理为金融组合风险对冲与工程设计提供抗震荡保障。

课程简介 / Description

This class is an applications-oriented course covering the modeling of large-scale systems in decision-making domains and the optimization of such systems using state-of-the-art optimization tools. Application domains include: transportation and logistics planning, pattern classification and image processing, data mining, design of structures, scheduling in large systems, supply-chain management, financial engineering, and telecommunications systems planning. Modeling tools and techniques include linear, network, discrete and nonlinear optimization, heuristic methods, sensitivity and post-optimality analysis, decomposition methods for large-scale systems, and stochastic optimization.

讲义 / Lecture Notes

• 1
  • Optimization Modelling and Computaional Issues in Radiation Therapy (PDF ‑ 1.5MB)
• 2
  • Increasing the Computational Effectiveness of the Simple Method (PDF)
  • Working with the Basis Inverse Over a Sequence of Iterations (PDF)
• 3
  • Applied Lagrange Duality for Constrained Optimization (PDF)
• 4
  • Simple Routines for Optimization (PDF - 2.2 MB)
• 5
  • Telecommunications System Design: Minimum-Cost Embeddings of Reliable Virtual Private Networks (PDF ‑ 1.5MB)
  • Exact Algorithms for the Minimum-Cost Embeddings of Reliable Virtual Private Networks into Telecommunications Networks (PDF)
• 6
  • Column Generation (PDF)
• 7
  • Column Generation II: Application in Distribution Network Design (PDF)
  • Shu, Jia, Zuo-Jun Max Shen, and Chung-Piaw Teo. "Stochastic Transportation-Inventory Network Design Problem."
  • Operations Research
  • 53: 48-60.
• 8
  • Module on Large-Scale Integer Programming and Combinatorial Optimization (PDF)
• 9
  • Introduction to Convex Constrained Optimization (PDF)
• 10
  • Facility Location and Distribution System Planning (PDF)
• 11
  • Network Design: Network Loading and Pup Matching (PDF)
  • Midterm Exam
• 12
  • Pattern Classification: Separable Problems
• 13
  • Pattern Classification, and Quadratic Problems (PDF)
• 14
  • Solution Methods for Quadratic Optimization (PDF)
• 15
  • E-commerce Application
• 16
  • Notes for Class: Analytic Center, Newton's Method, and Web-Based ACA (PDF)
• 17
  • Truss Design and Convex Optimization (PDF)
• 18
  • Issues in Non-Convex Optimization
• 19
  • Stochastic Linear Optimization, and Extensions (PDF)
• 20
  • Optimization under Uncertainty (PDF)
• 21
  • Benders' Decomposition Methods for Structured Optimization, including Stochastic Optimization (PDF)
• 22
  • Introduction to Semidefinite Programming (SDP) (PDF)
• 23
  • Truss Structures - Natural Frequency Manipulation via SDP (PDF ‑ 1.5MB)
  • Smith, Jeffrey, Jessica Hodgins, Andrew Witkin, and Irving Oppenheim. "
  • Creating Models of Truss Structures with Optimization
  • ."
  • ACM Transactions on Graphics (TOG)
  • 21, no. 3 (2002): 295-301.
• 24
  • Selfish Routing in Capacitated Networks (PDF)
  • System-Optimal Routing of Traffic Flows with User Constraints in Networks with Congestion (PDF ‑ 1.4MB)
  • Effective Route Guidance in Traffic Networks (PDF)
  • Effective Route Guidance in Traffic Networks (cont.) (PDF)

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