Operations Research (2): Optimization Algorithms
National Taiwan University
You probably have used some solver / optimizer software to solve problems, this wonderful course will show you what is under the hood. Being able to comprehend what has happened is crucial to customize the algorithms or even to develop your own ones.
There is a warm-up at the beginning: some basics like Gaussian elimination and the method to solve the inverse of a matrix, making sure you could manipulate matrices without pulling your hair out.
One. The first “main dish” is the Simplex method, which is a profoundly popular algorithm for linear programming. Simply put the whole thing is converting the linear program into the standard form, then from here on, search among basic feasible solutions until you find the optimal one. It is not necessary to memorize every steps, but important is to appreciate the beauty and power of matrix.
Two. We all know that solving an integer program is much slower than solving a similar linear program, the lecture of “branch-and-bound” elaborates the reason why. Based on linear relaxation, solving an integer program actually is like solving a tree of linear sub-problems.
Three. Compared to the linear and integer programming, non-linear programming uses rather different approaches: Gradient decent and Newton’s method. The former one sounds more familiar to those machine learning practitioners, the latter one is more frequent in the field of numerical analysis. This module aroused my interest in further studying of numerical methods.
Lastly the course covered a case study of heuristic algorithm. This is very helpful to those who thought the word ‘heuristic’ is too abstract. For some unexpectedly complicated problems, heuristic algorithms probably will be the only option.
It is also exciting that the course covers the celebrated solver Gurobi. You will need to write code in Python to finish homework.
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