Discrete Optimization: Linear Programming
Invented by George Dantzig in 1947, Linear Programming is one of the most fundamental tools in combinatorial optimization. You...
Discrete Optimization: Local Search
Previously we talked about constraint programming, which actually works with partial assignments, we try to extend them, and...
Discrete Optimization: Constraint Programming
Constraint Programming is one of the main paradigms to actually tackle optimization problems. The idea is to look...
Discrete Optimization: Knapsack Problems
Filling a knapsack is an NP-hard optimization problem, it is widely believed that in the worst case it...
My 130th certificate from Coursera
Operations Research (3): Theory National Taiwan University What a long journey, but totally worth it! The theory taught...
Operations Research: The Theory for Regression and SVM
The theory of Operations Research has been used to develop models in many fields like statistics and machine...
Lagrangian Duality and KKT Condition
In the case of unconstrained non-linear programs, we may determine whether the objective function is convex and then...
Convex Analysis
Compared with linear programs, non-linear programs (NLPs) are much more difficult to solve. In an NLP, a local...
Minimum Cost Network Flow
Network flow models are one specific format of mathematical programs. These are used to study operations that are...
Sensitivity Analysis and Dual Simplex Method
Previously, we mentioned that an sensitivity analysis tool called Shadow Price is helpful to evaluate the impact of...
Linear Programming Duality
When you are given a linear program, in many cases we call it a primal linear program. It...
Matrix Presentation of Simplex Method
When it comes to Operations Research, we are mainly talking about optimization problems, so the theories are mainly...
My #82 course certificate from Coursera
Operations Research (2): Optimization AlgorithmsNational Taiwan University You probably have used some solver / optimizer software to solve...
Heuristic Algorithms: A Case Study
The objectives for any research is that we want to build a mathematical model to formulate the given problem. The...
Non-Linear Programming: Gradient Descent and Newton’s Method
Non-Linear Programs When visualizing a linear program, its feasible region looks like a polygon. Because the objective function...