Convex Analysis and Optimization

Video lectures presented by Dr. Mau Nam Nguyen

This series of video lectures features the theory of convex analysis in finite dimensions and applications to optimization. The lectures are based on my recently published book “An Easy Path to Convex Analysis and Applications” (co-authored with Boris Mordukhovich) published by the Morgan & Claypool in 2013. Important topics of convex analysis such as subgradients, subdifferential calculus rules, Fenchel conjugate, differentiability of convex functions, and applications are presented with detailed proofs.

During this video project, Dr. Mau Nam Nguyen was partly supported by the National Science Foundation and the Faculty Development Program at Portland State University.

Chapter 1: Convex Sets and Functions

1.1 Preliminary
1.2 Convex Sets
1.3 Convex Functions
1.4 Distance Functions
- Part 1
- Part 2

Chapter 2: Subdifferential Calculus

2.1 Convex Separation
2.2 Normal Cones to Convex Sets
- Part 1
- Part 2
2.3 Subgradients of Convex Functions
- Part 1
- Part 2
2.4 The Subdifferential Sum Rule
- Part 1
- Part 2
2.5 The Subdiffential Chain Rule
- Part 1
- Part 2
2.6 The Subdiffential Maximum Rule
- Part 1
- Part 2

Chapter 3: Other Consequences of Convexity

3.1 Continuity of Convex Functions
- Part 1
- Part 2
3.2 Fenchel Conjugates
3.3 Directional Derivatives of Convex Functions
- Part 1
- Part 2
3.4 Subdifferential Characterization for Differentiability
- Part 1
- Part 2

Chapter 4: Applications to Optimization

4.1 Lower Semicontinuity and Existence of Minimizers
4.2 Optimality Conditions and the Method of Lagrange Multipliers

Chapter 5: Convex Numerical Algorithms

5.1 The Subgradient Algorithm
- Part 1
- Part 2
5.2 The Gradient Algorithm
- Part 1
- Part 2
5.3 Nesterov's Accelerated Gradient Method
- Part 1
- Part 2

Report abuse