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Does anyone knows a book about optimization that starts from the very basic calculus optimization, i've searched for it but they sometimes assume you have that basic knowledge, starting from linear optimization, quadratic optimization and lagrange multipliers.

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what kind of optimization?? –  Alex R. Apr 15 '12 at 4:39
may be Lagrange Multiplier would do? –  FiniteA Apr 15 '12 at 7:03
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3 Answers

I recommend the following books in ascending order

Stage 1

Winston, WL 2004, Operations research: applications and algorithms, 4th edn, Thomson Brooks/Cole, Australia. Hillier, F & Lieberman, G 2005, Introduction to operations research, 8th edn, McGraw-Hill, Boston.

Kolman, B & Beck, R 1995, Elementary linear programming with applications, 2nd edn, Academic Press, San Diego.

Taha, HA 2006, Operations research: an introduction, 8th edn, Prentice-Hall, Upper Saddle River, NJ.

Stage 2

Stephen Boyd's Convex Optimization

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I think this one is a good introductory book about optimization:

  • Sundaram, R.K., A First Course in Optimization Theory, Cambridge University Press, 1996.

It starts with mathematical preliminaries and goes through optimization in $R^n$, unconstrained optima, equality constraints and the Theorem of Lagrange, inequality constraints and the Theorem of Kuhn and Tucker, convex structures and so forth.

You can find it on Amazon or Google books, for example, and give a look at the complete table of contents.

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This is, by far, the best Linear Programming introduction (and more):

Chvátal, V. (1983). Linear Programming. W.H. Freeman. ISBN 978-0716715870.

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Understanding and Using Linear Programming Jiri Matoušek, Bernd Gärtner (2007) - less shrubbery. –  Peter Sheldrick Aug 14 '12 at 13:46
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