ELEC5470/IEDA6100A - Convex Optimization
Fall 2019-20, HKUST
In the last three decades, a number of fundamental and practical results have been obtained in the area of convex optimization theory. It is a well-developed area, both in the theoretical and practical aspects, and the engineering community has greatly benefited from these recent advances by finding key applications.
This graduate course introduces convex optimization theory and illustrates its use with many applications where convex and nonconvex formulations arise. The emphasis will be on i) the art of unveiling the hidden convexity of problems by appropriate manipulations, ii) a proper characterization of the solution either analytically or algorithmically, and iii) multiple practical ways to approach nonconvex problems.
The course follows a case-study approach by considering recent successful applications of convex optimization published within the last decade in top scientific journals in the areas of signal processing, finance, machine learning, and big data. Problems covered include portfolio optimization in financial markets, filter design, beamforming design in wireless communications, classification in machine learning, circuit design, robust designs under uncertainty, sparse optimization, low-rank optimization, graph learning from data, discrete maximum likelihood decoding, network optimization, distributed algorithms, Internet protocol design, etc.
- Boyd and L. Vandenberghe, Convex Optimization, Cambridge University Press, 2004.[https://web.stanford.edu/~boyd/cvxbook]
- Daniel P. Palomar and Yonina C. Eldar, Convex Optimization in Signal Processing and Communications, Cambridge University Press, 2009.
Students are expected to have a solid background in linear algebra. They are also expected to have research experience in their particular area and be capable of reading and dissecting scientific papers.
|Final Project:||60%||(homeworks and midterm are required to be passed)|
|2||Theory: Convex sets and convex functions|
|16-Sep||2||3||Theory: Convex problems and taxonomy (LP, QP, SOCP, SDP, GP)|
|4||Application: Filter design|
|23-Sep||3||5||Theory: Numerical algorithms – interior point method|
|6||Theory: Disciplined convex programming - CVX|
|30-Sep||4||7||Theory: Lagrange duality and KKT conditions|
|8||Application: Waterfilling solutions|
|14-Oct||5||9||Application: Markowitz portfolio optimization|
|10||Theory&Application: MM-based algorithms|
|21-Oct||6||11||Application: Risk parity portfolio in finance|
|12||Theory&Application: Geometric programming (GP)|
|28-Oct||7||13||Application: Sparsity via l1-norm minimization|
|14||Application: Sparse index tracking in finance|
|4-Nov||8||- Midterm -|
|6pm-9pm 18-Nov Rm5508||9||15||Application: Classification and SVM in machine learning|
|16||Application: Low-rank optimization problems (Netflix, video security)|
|3-4:30pm 20-Nov Rm4621||10||17||Application: Robust optimization with applications|
|3-4:30pm 22-Nov Rm4621||18||Application: Graph learning from data|
|6pm-9pm 25-Nov Rm5508||11||19||Application: ML decoding via SDP relaxation|
|20||Application: Rank-constrained SDP and multiuser downlink beamforming|
|3-4:30pm 27-Nov Rm4621||12||21||Theory: primal/dual decomposition techniques|
|3-4:30pm 29-Nov Rm4621||22||Application: The Internet as a convex optimization problem|
Lecture Time: Mon 18:00 – 20:50
Lecture Venue: CYTG009A (next to Subway)
Instructor: Prof. Daniel P. PALOMAR (https://www.danielppalomar.com)
Office: 2398 (Lifts 17/18)
Office hours: By email appointment
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