MA5037: OPTIMIZATION METHODS AND APPLICATIONS, Fall 2025

Instructor: Prof. Suh-Yuh Yang (楊肅煜)

• Office: M315, Hong-Jing Hall 

• Phone: 03-4227151 ext. 65130

• E-mail address: syyang@math.ncu.edu.tw

• Homepage: http://www.math.ncu.edu.tw/~syyang/

Office Hours: Tuesday 10:00~12:00 am or by appointment. 

Prerequisites: (Advanced) Calculus, Linear Algebra, Numerical Analysis, and some knowledge of programming language Matlab.

Textbook: Amir Beck, Introduction to Nonlinear Optimization: Theory, Algorithms, and Applications with Matlab,

                 MOS-SIAM Series on Optimization, SIAM, 2014. 

Course Objective: This course will provide the foundations of the theory of nonlinear optimization as well as some related algorithms and will present a variety of applications from diverse areas of applied sciences. This course combines three pillars of optimization: theoretical and algorithmic foundation, familiarity with various applications, and the ability to apply the theory and algorithms on actual problems.

General Information: This course will cover the following topics

Chapter 1: Mathematical preliminaries
Chapter 2: Unconstrained optimization
Chapter 3: Least squares
Chapter 4: The gradient method
Chapter 5: Newton’s method
Chapter 6: Convex sets
Chapter 7: Convex functions
Chapter 8: Convex optimization
Chapter 9: Optimization over a convex set
Chapter 10: Linearly constrained problems
Chapter 11: The Karush-Kuhn-Tucker conditions
Chapter 12: Duality

Assignments: approximately every two weeks, will consist of theoretical problems or computer projects.

Course Transparency Set: (in PDF)

• syllabus and introduction

• mathematical preliminaries

• unconstrained optimization

• least squares problem

• gradient method

• newton method

• convex sets

• convex functions

• convex optimization

• optimization over convex

• optimality conditions

• KKT conditions

• duality