CSE 291C, Spring 2020 Topics on Numerical Methods for Engineering

University of California, San Diego

Instructor

• CK Cheng, Office: CSE2130, email: ckcheng+291@ucsd.edu, tel: 858 534-6184
• Office hour: TBA

Teaching Assistant

• Po-Ya Hsu, p8hsu@ucsd.edu
• Office hours: TBA

Discussion Forum

• TBA

Schedule

• Lectures: 3:30-4:50PM TTH, Virtual Room: Zoom or Google hangout

References

• Electronic Circuit and System Simulation Methods, T.L. Pillage, R.A. Rohrer, C. Visweswariah, McGraw-Hill, 1998
• Convex Optimization Algorithms, D.P. Bertsekas, Athena Scientific, 2015.
• 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.
• Matrix Computations, G.H. Golub and C.F. Van Loan, Fouth Edition, Johns Hopkins, 2013
• Convex Optimization, S. Boyd and L. Vandenberghe, Cambridge, 2004
• Funcions of Matrices: Theory and Computation, N.J. Higham, SIAM, 2008.

Prerequisite

Basic knowledge of linear algebra, numerical methods, convex optimization, or intention of conducting projects related to scientific computation.

Content

The class covers topics on numerical methods for engineering. Students are encouraged to carry out the state of the art projects with team members. We intend to cover two parts according to the progress of the class. For part I, we talk about the dynamic system to model the system in high dimensional space with temporal behavior. The techniques of matrix solvers, integration methods, and sensitivity will be discussed. For part II, we study the optimization methods of convex problems. The algorithms of gradient/subgradient descent, approximation, and proximal approaches will be reviewed.

Lecture Notes, Part I: Dynamic Systems

• 1. Introduction pptx.
• 1.1. Motivation ppt.
• 2. Formulation ppt.
• 3. Matrix Solvers:
• (1) Sparse direct method by Xiaoye Sherry Li, ppt
• (2) Steepest descent methods ppt,
• Conjugate gradient tutorial by CK Cheng pdf,
• Nesterov Method: Differential Equation by Su, Boyd and Candes. pdf,
• Nesterov Method: Gradient and Mirror descent by Zhu and Orecchia pdf,
• Graident descent survey by S. Ruder: https://arxiv.org/pdf/1609.04747.pdf
• (3) Krylov subspace methods and multigrid methods ppt.
• 4. Integration:
• (1) One step methods pptx,
• (2) Multistep methods pptx.
• 5. Sensitivity: pptx,

Lecture Notes, Part II: Convex Optimization Methods (lecture notes by D.P. Bertsekas, Term of Use: http://ocw.mit.edu/terms.)

• 1. Introduction pdf
• 2. Overall view pdf
• 3. Subgradient methods
• I pdf
• II pdf
• 4. Approximation methods pdf
• 5. Proximal methods
• I. pdf
• II pdf
• ADMM by R. Tibshirani pdf
• III pdf
• 6. Advanced Approaches
• Extension of gradient projection methods I pdf
• Extension of gradient projection methods II pdf
• Extension of incremental methods pdf
• Extension of proximal methods pdf
• Distributed asynchronous methods pdf

Integer Programming

• Integer Programming by Larrosa, Oliveras, and Rodriguez-Carbonell, pdf
• Integer Programming by Kolter and Shah, pdf
• Integer Programming by Cornuejols, Trick and Saltzman, pdf

Project

• Project Outlines (what are we looking for?) pdf, pptx.