最佳化理論與應用

This course will focus on convex optimization, which has been used in efficiently solving many signal processing and communications problems, thanks to the development of interior point method (IPM), specifically the primal-dual IP algorithm. The course will include both 1) problem modeling (formulation), i.e. recognizing if a problem is convex, and if possible, turning a seemingly nonconvex problem into a convex one, and 2) learning the algorithms, mainly the IPM and its variations, that can efficiently solve the problem. Due to the large amount of content we need to cover, some of the materials will be taught offline via video. We will NOT be covering integer nor mixed-integer convex programming, nor problems that involve nondifferentiable functions, which may require the use of subgradient and subgradient methods. However, individual discussions can be held based on the student's research needs. Unlike previous years, the lecture this semester will be SUPPLEMENTED by video that are accessible from the course website. Regular lectures will still be given in-class on Friday. Assignments will be done in-class and in groups determined a priori to the first assignment. The assignments will be done during Wednesday's lectures.

Linear Algebra, Probability and Statistics. Background in Linear Programming and/or Real Analysis will helpful but not required.

https://mcube.lab.nycu.edu.tw/~cfung/courses/2025_2026/optim/

-- Written Assignment (0%) --.Optional. -- Matlab Assignment (20%) -- Due time depending on assignments. -- Each day late will result in 50% reduction of the full grade. -- Final project (20%) -- Group project (group of 1-2) that 1) solves a new nonconvex optimization problem, OR 2) performs an in-depth review of a topic that involves the use of convex optimization. -- Class Participation (0-10%) -- Given to students who 1) actively participate in class, for example, raising good questions, and 2) borderline in terms of grades. -- No credit will be given for simply showing up. -- Midterm (30%) -- Length: 2 hour exam. -- Scope: Covers everything from beginning of the course until Ch 3 of [CLL17,BV04] (inclusive). -- Closed books. Calculator and A4-size handwritten sheet (2-sided) are allowed. -- Final (30%) -- Length: 2 hour exam. -- Scope: Comprehensive. -- Closed books. Calculator and A4-size handwritten sheet (2-sided) are allowed.

-- Textbook : CONVEX OPTIMIZATION FOR SIGNAL PROCESSING AND COMMUNICATIONS, by C.-Y. Chi, W.-C. Li, and C.-H. Lin, CRC Press, 2017. - Selected topics from Ch. 1-10 will be covered. - Referred to as CLL17 CONVEX OPTIMIZATION, by S. Boyd and L. Vandenberghe, Cambridge University Press, 2004. - Selected topics from Ch. 1-5, 9-11 will be covered - Referred to as BV04 -- References: CONVEX OPTIMIZATOIN THEORY, by D.P. Bertsekas, Athena Scientific, 2009. NONLINEAR PROGRAMMING, 2ND Ed., by D.P. Bertsekas, Athena Scientific, 1999. The list below is more focused on algorithms AN INTRODUCTION TO OPTIMIZATION, 4th Ed., E.K.P. Chong and S.H. Zak, Wiley, 2013. NUMERICAL OPTIMIZATION, 2nd Ed., by J. Nocedal and S.J. Wright, 2nd Ed., Springer, 2000.

地點

ED 639

時間

by appointment

聯絡方式

email: c.fung@ieee.org x31862