Sharif University of Technology

**Numerical Optimization**

- TO BE PRINTED FOR THE LAST SESSION OF THE COURSE: Heuristic methods for Optimization.
- Line-Search Algorithms.
- LOCATION of the Midterm Exam: Alef-17.
- Proof of Necessary Conditions using P1->P2.
- Proof of Second-Order Necessary Conditions (SONC).
- Proof of 2nd order local convergence of Newton.
- Convergence of the Steepest Descent algorithm with ideal step-size.
- A summary on the concept of condition number of square matrices.
- Time of the TA class: All Tuesdays, from 16:30 to 18, in IbnSina-24.
- Comparison of definitions of the order of convergence in our text books.
- Time of the Midterm Exam: Wednesday 24 Aban 1396, from 13:30 to 16:30.

- Homework 8:
- Type: Programming.
- Implement the BFGS method (with your line-search algorithm of the previous homework), and re-run Homework 4 using this new code and compare the results.
- Due date: Sunday 10 DAY 1396.

- Homework 7:
- Type: Programming.
- Implement the line-search algorithm based on Strong Wolfe conditions, and re-run Homework 4 using this line-search (instead of GSS) and compare the results.
- Due date: Tuesday 28 AZAR 1396 -> Extended to Sunday 3 Day 1396.

- Homework 6:
- Chong's book (2nd Edtion), problems 20.4(b,c), 20.5(a,c), 20.8, 20.16, 20.17, 20.18.
- Due date: Tuesday 23 Aban 1396.

- Homework 5:
- Chong's book (2nd Edtion), problems 20.1(a,c), 20.2, 20.4, 20.6, 20.7, 20.10 (Quadratic Programming), 20.16.
- Due date: Tuesday 16 Aban 1396.
- For yourselves: 20.5(a,c), 20.16, 20.17.

- Homework 4. (type: Programming) Due date: Tuesday 2 Aban 1396.
- Homework 3. (type: Manual) Due date: Tuesday 25 Mehr 1396.
- Homework 2. (type: Manual) Due date: Tuesday 18 Mehr 1396.
- Homework 1. (type: Programming) Due date: Tuesday 4 Mehr 1396.

- Jorge Nocedal and Stephen Wright, "Numerical Optimization," Springer, 2006.
- R. Fletcher, "Practical Methods of Optimization," Wiley, 1988.
- Dimitri P. Bertsekas, "Nonlinear Programming", 2nd Edition, Athena Science, 1995.
- Edwin K. P. Chong and Stanislaw H. Zak, "An Introduction to Optimization," Wiley, 2001.
- David G. Luenberger, " Linear and Nonlinear Programming," Addison-Wesley.

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