COURSE TOPICS OUTLINE - C &O 370

• Major Topics
  • Sub-topics
    • Resources for the different topics are included.

• Mathematical Programming ( Chapter 1)
  • Introduction to Operations Research
    History, Impact, Careers, Software.
  • An Overview of Modeling
    Formulation, Constructing a Model, Solution, Testing, Implementation.
    • What experts think about, (from T.R. Willemain, Operations Research, vol 43, 1995.)
  • Related Resources:
    • Systems Analysis laboratory, with lots of applications and modelling; and applied problems.
    • Optimization Technology Center, contains library, technology, guide. Solves problems on line. See their optimization tree It introduces the different subfields of optimization and includes outlines of the major algorithms in each area, with pointers to software packages where appropriate.
• Linear Programming, LP, Review
  • The - Revised Simplex Method and Bounded Variable Simplex Method ( Chapter 2 & Appendices A & B)
  • Duality ( Chapter 4: 4.1-4.6 and 4.8)
  • Sensitivity Analysis ( Chapter 3)
    economic interpretations
    • example of parameter sensitivity analysis (Australian budget)
  • Related Resources:
    • Linear Programming at the Optimization Technology Center.
    • FAQ (frequently asked questions) on linear programming
    • The Diet Problem: An Application of Linear Programming, a description, software, etc... (from Jon Lee).
• Network Programming ( Topics from Chapter 8)
  • Models of Production & Transportation
  • Network Flow Problems
    • shortest path, maximum flow problems
    • Information and Software on Network Models
    • a bibiliography on network flow problems
    • Linear Network Optimization at NEOS.
    • outline of the network simplex algorithm,
  • Sensitivity Analysis
    • Traffic-Sensitivity Analysis
• Dynamic Programming ( Topics from Chapter 11)
  • Models of Replacement & Allocation
  • Path Problems & Recursive Computation
• Integer Programming ( Sections 9.1-9.4)
  • Binary Variables, logistical equations
  • Cutting Stock (delayed column generation) (Chvatal, pgs 195-200)
  • Cutting Planes
    • global optimization web page by Arnold Neumaier
• Nonlinear Programming, NLP( Chapter 13, 13.1-13.4, 13.7-13.8)
  • Sample Models, Local and Global Optimum, Convex Functions
  • Lagrange Multipliers
    • local notes on Lagrangian Methods, (originally from Richard Weber)
    • local notes on Lagrangian duality, (originally from Richard Weber)
    • local notes on sensitivity analysis for Lagrangian duality, (originally from Richard Weber)
    • Course Notes by Richard Weber - complete contents at Cambridge
  • Lagrangian Duality
    • Course Notes by Boyd and Vandenberghe
  • Applications to LP and Quadratic Programming, QP
  • Related Resources:
    • general constrained optimization problem description at NEOS.
    • FAQ (frequently asked questions) on nonlinear programming
    • Introduction to Convex Optimization, course notes by Boyd and Vandenberghe, including Lagrangian duality, LP duality, interior-point methods, and semidefinite programming.
• Semidefinite Programming, SDP
  • description of SDP at the OTC.
  • SDP home page, organized by Christof Helmberg.
  • SDP lecture notes , organized by Farid Alizadeh.
  • Background and Applications of SDP
  • Duality for SDP
    • Introduction to Convex Optimization, course notes including semidefinite programming.
• Algorithms and Software - Topics from all the above
  • Newton's Method ( Section 13.9)
    • Newton-Raphson method online lessons at the University of Utah.
  • Primal-Dual, Interior-Point Algorithms for LP and SDP ( Section 13.8)
    • miscellaneous software and papers
    • semidefinite programming software and related papers.
  • Column Generation and Decomposition for large scale LPs ( Sections 9.1-9.4)
  • Branch-and-Bound
    • public domain codes
  • Implicit Enumeration knapsack problem