CSE 291, Winter 2017 Convex Optimization

University of California, San Diego

Instructor

• CK Cheng, ckcheng+291@ucsd.edu, 858 534-6184

Schedule

• Lectures: 12:30-1:50PM TTH, Room CSE2154

References

• Convex Optimization, S. Boyd and L. Vandenberghe, Cambridge, 2004 (required textbook).
• Numerical Recipes: The Art of Scientific Computing, Third Edition, W.H. Press, S.A. Teukolsky, W.T. Vetterling, and B.P. Flannery, Cambridge University Press, 2007.
• Funcions of Matrices: Theory and Computation, N.J. Higham, SIAM, 2008.
• Fall 2015, Convex Optimization by R. Tibshirani, http://www.stat.cmu.edu/~ryantibs/convexopt/
• EE364a: Convex Optimization I, S. Boyd, http://stanford.edu/class/ee364a/

Prerequisite

Basic knowledge of numerical methods or intention of conducting projects related to scientific computation.

Assignment and Grading

Grading is based on class participation, 6 to 8 exercises and a project with final presentation.

Content

We study the formulations and algorithms solving convex optimization problems. The topics include convex sets, functions, optimality conditions, duality concepts, gradient descent, conjugate gradient, interior-point methods, and applications. The objective of the course is to provide students the background and techniques for scientific computing and system optimization.

Extra Materials

• Conjugate Gradient Tutorial by CK Cheng.
• Nesterov Method: Differential Equation by Su, Boyd and Candes.
• Nesterov Method: Gradient and Mirror Descent by Zhu and Orecchia.

Exercises from Convex Optimization by Boyd and Vandenberghe, additional exercises (Ax.x) and data files: http://stanford.edu/~boyd/cvxbook/

• Exercise 1: Due 1/24/2017: 2.8, 2.10, 2.12, 2.24a, 2.25, 2.31, A1.5 and possible assignment in the class. (A1.5 in http://stanford.edu/~boyd/cvxbook/bv_cvxbook_extra_exercises.pdf)
• Exercise 2: Due 2/9/2017: 3.1, 3.2, 3.13, 3.14, 3.40, and A2.9, A2.18. Note that for A2.18, try f*((A+) y) instead of f*((A+)T y).
• Exercise 3: Due 2/16/2017: 4.1, 4.11, 4.12, 4.28, and A3.2, A3.4.
• Exercise 4: Due 2/23/2017: 5.1, 5.18, 5.21, 5.31 and A4.1, A4.10.
• Exercise 5: Due 3/2/2017: 9.1, 9.7, 9.9, and 9.30+A8.3, 9.31+A8.4.
• Exercise 6: Due 3/9/2017: 10.1, 10.15, 11.7, and 11.12.

Project

• Outlines (title, motivation, statement of the problem, wish list, references) due 2/16/2017.