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...
My #81 course certificate from Coursera
Vector Calculus for EngineersThe Hong Kong University of Science and Technology We can’t emphasize enough the importance of...
My #80 course certificate from Coursera
Differential Equations for EngineersThe Hong Kong University of Science and Technology By highlighting both theories and applications in...
Vector Calculus: Fundamental Theorems
Gradient Theorem The fundamental theorem of single variable calculus was the one that told you “the integral of the...
Line and Surface Integrals
Line Integrals Scalar Fields We have a curve C in the x-y plane, we can represent a point...
My #79 course certificate from Coursera
Logic for EconomistsUniversity of Amsterdam The logo of University of Amsterdam is cool, so is this succinct course....
The Diffusion Equation of a Dye
Fourier Series Sometimes complicated motions can actually be composed of motions of many different frequencies. The type of mathematical analysis...
Systems of Differential Equations
Systems of Homogeneous Linear First-order ODEs The system of linear first order homogeneous equations can be written in matrix...