I want to learn optimization for implementation in my Ph.D. research project. I have no idea if I should start with linear programming, non-linear programming, convex or concave optimization?
Any idea?
First read about classical optimization methods from popular books. To learn about advanced optimization techniques, attend Short-Term-Training-Programs from IITs or NITs.
Start with Linear Programming, it is the easiest way to learn what optimization is.
You can even solve a simple 2D problem using a graphic in a couple of minutes
I would start by searching - via Google - for tutorials, especially powerpoint/pdf presentations from classes on mathematical optimization and operations research, on topics like linear programming, nonlinear programming, integer programming, network optimization, and integer and combinatorial optimization. Since much of these themes can be illustrated well by using graphical representations, you can learn quite a lot already from class tutorials.
Starting with LP after understanding convex, concave functions, local, global optimum definitions, is the right way. For beginning you may read Hillier & Liberman...very good book to understand LP. After LP you may go to NLP and DP etc. Online tutorials and video lectures will also be helpful...(e.g., you may follow Lecture Series on Fundamentals of Operations Research by Prof.G.Srinivasan, Department of Management Studies, IIT Madras) . good luck for your research project!
Optimization Methods by S.S.Rao is a good book to start with for both nonlinear and linear programming problems. If you want advanced learning in Linear Programming then Hamdy A Taha is a good one to start in modeling. For nonlinear programming problems Bazaraa and Shetty is a wonderful book. In addition you need to equip with the use of computer packages TORA, LINGO, Mathematica etc.
The book of Boyd and Vandenberghe: Convex Optimization is a good source. The book is available online Stephen Boyd's website.
With best regards,
Jacek Gondzio
In my opinion, the best basic book for optimization for beginners is "Numerical Optimization" from Nocedal&Wright. You can find it in any good library.
The best way, I think, is to read and use Nigel SLACK & alii's about Operations Management.
As a side note - or indeed question: what topic - or topics - has your supervisor(s) asked you to study? That might be a very good thing for us to know, such that we can give you more accurate suggestions! :-)
You might find this link useful.
https://neos-guide.org/optimization-tree
I agree with Mr. Mitra especially on his last paragraph.
Which is the field you are particularly interested on?
Maybe these online courses will help you:
https://www.coursera.org/learn/advanced-algorithms-and-complexity
https://www.coursera.org/learn/discrete-optimization
Also, Syed, hasn't your advisor mentioned in a bit more detail which field within optimization you will work in? It would be easier for us to suggest books then. You may not know this, but there are hundreds of basic books in the field (only in my office there are in the order of 600 books!), and you might pick the wrong one if you do not check the contents of the book you will buy.
So if you have anything to say about topics we might be better att providing hints. :-)
Syed
A week ago I suggested you the sane as Michael does now. Mathematical Programming is a very wide field and it would be easy for us to give you some advice if we know what field you are interested in
Dear Nolberto Munier,
Thanks for your reply. Let me go to university tomorrow and brush off some dust on my brain coz of vacations. I will get back to you. Thank you very much.
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