Into the Unknown
Operations Research (3): Theory National Taiwan University What a long journey, but totally worth it! The theory taught in this course is critical, beautiful, powerful. Whatever fields or industry you are in, statistics, machine learning, economics, logistics, etc. This course definitely will help you consolidate the foundation for all skills you need to be professional….
The theory of Operations Research has been used to develop models in many fields like statistics and machine learning. Linear Regression We try to find 伪 and 尾 such that a line g = 伪 + 尾 x to minimize the sum of squared errors for all the data points: Despite the word linear in…
In the case of unconstrained non-linear programs, we may determine whether the objective function is convex and then use the first order condition (FOC) to find all local minima. However in practice, most of the time, nonlinear programs are constrained. We can not simply ignore those constraints treating the program as an unconstrained, and then…
Compared with linear programs, non-linear programs (NLPs) are much more difficult to solve. In an NLP, a local minimum is not always a global minimum. A greedy search method like gradient decent may be trapped at a local minimum. Also even the NLP has optimal solutions, these optimal solutions may exist on a boundary, but…
Network flow models are one specific format of mathematical programs. These are used to study operations that are related to network transportation. A unified model, called Minimum Cost Network Flow (MCNF) covers many network operations. MCNF is a special form of linear program or integer program. Even better, MCNF has a very nice property: once…
Previously, we mentioned that an sensitivity analysis tool called Shadow Price is helpful to evaluate the impact of change when right hand side value of a constraint is increased by 1. However in some cases, there might be new variables or new constraints added, the good news is you don’t have to solve the problem…
When you are given a linear program, in many cases we call it a primal linear program. It is usually going to be able to find another program, called a dual linear program. The primary reason why we want to use duality is that the computation time of the simplex method is roughly proportional to…
When it comes to Operations Research, we are mainly talking about optimization problems, so the theories are mainly optimality conditions. They basically mean for an optimization problem, somehow there should be an optimal solution. We want to get the conditions which will make the optimal solution satisfy. Typically we search for the necessary conditions, while…