Continuous Optimization - 466/666 - Winter 1997

This course provides a rigorous up-to-date treatment of topics in Continuous Optimization (Nonlinear Programming). This includes a hands-on approach with exposure to existing software packages.

Contents

Conduct of Course

  • Instructor:
  • Office Hours:
  • Lectures:
  • Text:
  • References:

    Additional References:
       
    1. Practical Optimization, P.E. Gill, W. Murray, M.H. Wright.
    2. Numerical Methods for Unconstrained Optimization and Nonlinear Equations, J.E. Dennis and R.B. Schnabel
    3. Nonlinear Programming: theory and algorithms, M.S. Bazaraa, C.M. Shetty, Sherali
    4. Linear and Nonlinear Programming, D.G. Luenberger, Second Edition
    5. Nonlinear Programming, Peressini, Sullivan, Uhl
    6. Practical Methods of Optimization, R. Fletcher
    7. Mathematical Programming Methods, G, Zoutendijk
    8. Nonlinear Programming, G.P. McCormick
    9. Mathematical programming : theory and algorithms, M. Minoux (QA402.5.M5613)
    10. Optimization by Vector Space Methods, D.G. Luenberger
    11. Convex Analysis, R.T. Rockafellar
    12. Theory of Extremal Problems, A.D. Ioffe and V.M. Tihomirov

  • Home Page, C&O 466/666, ftp://orion.uwaterloo.ca/pub/henry/teaching/w97/666.w97/readme.html
  • Term Work:
      will consist of homework problems . (See attached schedule of assignments.)
  • Final Exam:
      A 3-hour exam, scheduled by the registrar.
      (Please see the detailed course outline for topics covered during the semester.)
  • Marking Scheme:
    • Homework............ 50%
    • Final Exam.......... 50%

    COURSE TOPICS OUTLINE - C &O 466/666

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

    HOMEWORK LIST- C &O 466/666

    • Homework #1 (Unconstrained Optimization)
      Due: Tuesday January 21
      Reading       Problems
      • Bertsekas, pp 15, #1.1.6 (Weber Point) and solution latex file.
      • Bertsekas, pp 51, #1.2.14 (Steepest Descent) and solution latex file1 and file2.
      • Bertsekas, pp 115 #1.5.3 (Gauss-Newton);
          Use the optimization technology center to solve a similar problem but with k randomly generated data points, k=50; if possible, discuss the solver that you used and the algorithm.
      • Bertsekas, pp 141 #1.7.2 (Limited Memory BFGS)
    • Homework #2 (Optimization Over a Convex Set)
      Due: Thursday February 6
      Reading Problems
      • Bertsekas, pp 187 #2.1.10 (Second Order Nec. Opt. Cond.)
      • Bertsekas, pp 188 #2.1.11 (Second Order Suff. Opt. Cond.)
      • Bertsekas, pp 190 #2.1.16 (Fractional Programming)
      • Bertsekas, pp 223 #2.3.8 (The Proximal Minimization Algorithm)
    • Homework #3 (Lagrange Multiplier Theory)
      Due: Thursday February 20
      Reading
      • Bertsekas, topics in Chapter 3
      Problems
      • Bertsekas, pp 271 #3.1.6 (The AGM Inequality)
      • Bertsekas, pp 291 #3.3.6 (Minimax)
      • Bertsekas, pp 309 #3.4.4 (Transportation Problem)
    • Homework #4 (Lagrange Multiplier Algorithms)
      Due: Tuesday March 11
      Reading
      • Bertsekas, topics in Chapter 4
      Problems
      • Bertsekas, pp 327 #4.1.1
        (Central Path - for the program, you can use OTC-NEOS)
      • Bertsekas, pp 360 #4.2.8 (Ill-Conditioning of Penalty Methods)
      • Bertsekas, pp 271 #4.3.4 (Exact Penalty Functions)
      • Bertsekas, pp 271 #4.3.9 (Maratos' Effect)
    • Homework #5
      Due: Thursday April 3
      Reading
      • Bertsekas, topics in Chapters 5 and 6
      Problems
      • Bertsekas, pp 436 #5.1.7 (Duality Gap for the Knapsack Problem)
      • Bertsekas, pp 450 #5.3.1 (Boundedness of Lagrange Multipliers)
      • Bertsekas, pp 530 #6.4.1 (Linear Problems with Coupling Variables)