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ECM5901 Optimization Theory and Application
Spring 2022
Institute of Communications Engineering
National Yang Ming Chiao Tung University
Instructor:
Office:
Office hours:
email:
Prof. Ching-Yi Lai
ED926
Wednesday 9:50-11:00am (or by appointment)
cylai@nycu.edu.tw
Lectures:
2BCD-EC015
TA:
√Z
office:ED717
office hour:Thursday 13:30-15:00
email:xdlaughhaha.eed06@nctu.edu.tw
Text:
Convex Optimization (Cambridge, 2004)
Stephen Boyd and Lieven Vandenberghe
Reference:
1. CVX: Matlab software http://cvxr.com/cvx/
2. Convex Optimization for Signal Processing and Communications:
From Fundamentals to Applications (CRC Press, 2017)
Chong-yung Chi, Wei-chiang Li, Chia-hsiang Lin
Course grade:
Homework (25%):
Midterm Exam (35%):
Final Exam (40%):
Required preparation:
seven to eight problem sets will be assigned at 1-2 week intervals
April 12, Tuesday 9:00-12:00
May 31, Tuesday 9:00-12:00 允
%
a basic understanding of probability theory and advanced analysis
and a good knowledge of linear algebra
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Convex optimization is a class of mathematical optimization problems, which includes least-square and
linear programming problems that can be efficiently solved.
The idea is to extend known tools for these two problems to a larger class of convex optimization
problems, such as semidefinite programming.
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Convex optimization has found applications in many areas, such as estimation and signal processing,
communications and networks, machine learning, circuit design, analysis, statistics, and finance, where
it is used to find optimal or approximate solutions.
The goal of this course is to develop a working knowledge for recognizing or formulating a problem
as a convex optimization problem, which can then be reliably and efficiently solved by well developed
numerical analysis tools.
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The following materials in [HV03] will be covered in this semester:
Chapter 1: Introduction
Chapter 2: convex sets
Appendx
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Chapter 3: convex functions
Chapter 4: convex optimization problems
-
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Chapter 5: duality theorem
Chapters 9, 10, 11: Algorithms
Applications of convex optimization could be found in Chapters 6, 7, and 8, which will be skipped due to
the time-limit.
Using CVX (Matlab software) http://cvxr.com/cvx/
1. Download. Example: download cvx-w64.zip if you are using Windows. Then unzip the file.
2. Execute MATLAB. Run cvx setup.m and cvx startup.m in MATLAB.
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