Convex Optimization Theory and Method

Introduction

    This course mainly introduces the basic theory of optimization and its typical problems, namely convex problems. The lecture begins with the classic gradient descent optimization. It covers mainly typical convex optimization problems such as linear programming (LP) and quadratic programming (QP). The general convex optimization theory is introduced, such as the convex set, convex functions, and convex problems, and the typical solutions for them. The typical optimization problems are introduced along with the optimization algorithms and their applications. This course also covers integer programming (IP) and stochastic optimization.

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Course Code: U10304800539, Lecturer: Dr. Wan-Lei Zhao
Syllabus and Lecture slides
        Lecture 1: Unconstrained Optimization for Differentiable Functions [slides] [lab1] [lab1 training data]
        Lecture 2: Introduction to Linear Programing [slides] [lab2] [Assignment 1]
        Lecture 3: Simplex Method [slides] [lab3] [Assignment 2] [lab4]
        Lecture 4: Two-Phase Method, Duality for LP [slides] [Assignment 3] [lab5]
        Lecture 5: Introduction to QP and Convex Set [slides]
        Lecture 6: Convex Fucntions [slides] [lab6] [Assignment 4]
        Lecture 7: Convex Problems [slides] [Assignment 5]
        Lecture 8: Lagrangian Multiplier [slides] [Assignment 6]
        Lecture 9: Lagrangian Dual and KKT Condition [slides]
        Lecture 10: Interior Point Method [slides]
        Lecture 11: Portfolio Problem [slides] [lab7] [data for lab7]
        Lecture 12: Support Vector Machine [slides] [lab8]
        Lecture 13: Integer Programming [slides] [Assignment 7] [lab9]
        Lecture 14: Stochastic Optimization [slides]