Deployment of large-scale Mathematical Optimization Models, Learn the up & coming optimization software 'Fico Xpress'

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- Created by Dr. Spyros Giannelos
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Description

Assume that you have $ 100,000 and you want to invest this money in 5 stocks. So you take a piece of paper and you write some mathematical equations. You say that X1 , X2 , X3 , X4 , X5 are 'variables' that represent the amount of money that you will invest in each of the 5 stocks. So the first inequalities are that: X1 >=0 , X2 >=0 , X3 >=0 , X4 >=0 , X5 >=0. Because the amount of money cannot be negative.

The second inequality/equation is that X1 + X2 + X3 + X4 + X5 = 100,000 , which means that you want to invest all of your money i.e. exactly $ 100,000. This is an equation. So an optimization problem includes equations and inequalities.

Also you have an 'objective'. You want to 'optimize' i.e. maximize, your profit from this investment. For example, you know that on average, each stock is expected to give you some return over the next year.

So if you invest $1 in Stock1 then you expect to end up with $ 1.5 in the end of the year. For Stocks 2,3,4,5 similarly you expect $2, $3, $4 and - $0.5 So you write: maximize 1.5*X1 + 2*X2 +3*X3 + 4*X4 - 0.5*X5. This is your 'objective'. So every 'optimization problem' has an objective : to maximize or minimize something.

Imagine that you have many many more equations and inequalities . For example you want that the average investment to be more than $10,000 i.e. (X1+X2+X3+X4+X5 ) /5 >= 10,000 . And imagine you have many many many more. So this problem becomes very large !

So the problem becomes hard to solve on paper. When we say 'solve' we mean to find the value of the variables X1, X2, X3, X4, X5, that make us meet our objective. So if we solve all the equations/inequalities we may end up with a solution that says X1 = $ 20,000 , X2 = $40,000 , X3 = $40,000, and X4=0 , X5=0. We call this 'optimal solution'.

So when we have really large optimization problems it is better to write these equations into a software such as the one I am teaching in this course. Then we simply press a button and the software after some time (eg 5 minutes, 10 minutes, 10 seconds) depending on how large the problem is, will find for us the optimal solution. There are many 'optimization languages' as we call them. FICO Xpress is one of them , and I find it very easy to learn, and this is why I am teaching it here. You can find other such software including GAMS, and MATLAB. I would recommend to test them all and see which one you prefer. Which one is easier to learn - which is more stable. Have a look for yourself!

So in this course we assume that you can translate a problem into equations. So we start from the assumptions that you have the equations / inequalities and you dont know how to write them in this software. So I am teaching the software. I also show you how to run the model and how to read the optimal solutions.

If you know how to develop optimization models (i.e. to write the code) you will benefit a lot.

For example, this skill finds application in finance in terms of identifying the optimal investment portfolio. Platforms such as Nutmeg run 'optimization models' because they try to find the optimal allocation of the stocks and bonds for you to maximize your profit. So if you want to find a job there, you will really benefit a lot if you add this skill on your CV.

It finds application in machine learning and in artificial intelligence. Because machine learning is all about making optimal predictions. See the word 'optimal' here.

It finds application in business, in terms of identifying the best decision i.e. the one that will maximize profits.

So, by purchasing this course, you get

------life-long access to the course and to the Q & A section. You can also contact me in private for any inquiries, collaborations and business suggestions.

------life-long access to the course that has more than 1000 students, most of which have experience in optimization and, therefore, you can benefit from exchanging ideas. It is like an optimization forum.

-----life-long access to updates; this course is a living organism , there will be new videos , new explanations, constant improvements etc.

Finally you can recommend your own ideas about future courses and subjects to deal with.

And , last but not least, thank you for your interest in the course. You definitely made the 'optimal' choice because investment in our knowledge and education is the best investment !