Sharif University of Technology

**Numerical Optimization**

- Final grades of the course.
- Grades of homeworks.
- Grades of midterm and final exams.
- TO BE PRINTED FOR THE LAST SESSION OF THE COURSE:Augmented Lagrangian and Barrier Algorithms, and Heuristic methods for Optimization.
- Invariancy of Optimization Algorithms.
- Line-Search Algorithms.
- LOCATION of the Midterm Exam: Barg-1,2,3. TIME: 9am to 12. (Date: Thursday 18 Azar 1395).
- 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.
- Comparison of definitions of the order of convergence in our text books.
- Time of the Midterm Exam: Wednesday 19 Aban 1395, from 13:30 to 16:30.

- Homework 7:
- 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: Tuesday 14 DAY 1395.

- Homework 6:
- 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 7 DAY 1395.

- Some selected problems (to be solved for yourselves): Chong's book, problems 20.5(a,c), 20.8, 20.16, 20.17, 20.18.
- 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 2 Azar 1395.
- For yourselves: 20.5(a,c), 20.16, 20.17.

- Homework 4. (type: Programming) Due date: Sunday 16 Aban 1395.
- Homework 3. (type: Manual) Due date: Tuesday 4 Aban 1395.
- Homework 2. (type: Manual) Due date: Tuesday 27 Mehr 1395.
- Homework 1. (type: Programming) Due date: Tuesday 13 Mehr 1395.

- 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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