Topics

We summarize here some highlighted posts in this blog.

1. Theoretical Mathematics

1. Duality Theorems in Optimization
2. Properties of Adjoint Operator
3. On the Duality Between Uniform Convexity and Uniform Smoothness
4. Biconjugate theorem for convex functions
5. An Introduction to Lambda Calculus
6. Submodular Optimization: Modular and Submodular Properties of the Sum and Max Functions
7. Parametric Optimization: On the Lower Semicontinuity of Parametric Optimization
8. Submodular Optimization: Topkis’ Theorem for Supermodular Functions
9. General Optimization: When Infimum Breaks a Familiar Equivalence in Optimization
10. General Optimization: Minimum Over Unions: A Distribution Property

2. Applied Mathematics

A. Machine Learning, Signal Processing:

• Solving L1-Penalization of Kullback-Leibler Divergence using SMART Algorithm
• Solving Blasso problem using gardient descent method
• Solving Elastic-Net problem using Proximal Gradient Descent
• Chambolle-Pock Algorithm for Solving LASSO
• Support Vector Machine (P1)
• Mathematical Definition of Image Classification Problem
• A deep understanding of PCA: From statistics to optimization explanation
• MNIST Classification using PyTorch’s Neural Network

B. Combinatorics:

• Solving Knapsack Problem with Python
• Solving Quickest Path Problem in Networks using Python
• Finding discrete local maximizers

C. Calculations:

• On the calculus of Kullback-Leibler Divergence
• Fenchel inequality with Proximal operator
• Product of Gaussian functions
• Projection onto L1 Unit Ball

D. Others:

• Linear Programming using Interior Point Method
• Steady state detection in time series analysis

3. Programming

1. How to plot spectrum
2. Create GIF image with Python
3. Using Python to plot the city graph of France
4. Plotting Region defined by Inequality Constraints in Python (Part 2)
5. A “Hello World” program using Asymptote - A Vector Graphics Language
6. Visualization of optimal transport
7. Introduction to NetworkX in Python
8. Image processing: Transforming MNIST digits using optimal transport
9. Using Support Vector Machines (SVM) to Classify the MNIST Dataset
10. Lasso Safe Screening for Feature Elimination
11. Shape Analysis: Skeleton of Point Cloud with Python