Intereting Posts

Solve $a^3 + b^3 + c^3 = 6abc$
prove that $f'(a)=\lim_{x\rightarrow a}f'(x)$.
How can you prove that the square root of two is irrational?
Does every uncountable real set touch a rational number?
How to prove that if $\det(A)=0$ then $\det(\operatorname{adj}(A))=0$?
Can a non-zero vector have zero image under every linear functional?
Proof of Jordan Curve Theorem for Polygons
If $a,b$ are positive integers such that $\gcd(a,b)=1$, then show that $\gcd(a+b, a-b)=1$ or $2$. and $\gcd(a^2+b^2, a^2-b^2)=1$ or $2 $
If $M$ is Noetherian, then $R/\text{Ann}(M)$ is Noetherian, where $M$ is an $R$-module
Prove that $14322\mid n^{31} – n$
Regularity up to the boundary
How to evaluate $\int_0^1\int_0^1 \frac{1}{1-xy} \, dy \, dx$ to prove $\sum_{n=1}^{\infty} \frac{1}{n^2}=\frac{\pi^2}{6}$.
Prove that $\sin^2(A) – \sin^2(B) = \sin(A + B)\sin(A -B)$
If $n$ is a positive integer, does $n^3-1$ always have a prime factor that's 1 more than a multiple of 3?
How to determine the existence of all subsets of a set?

for somebody having a quite strong background in Mathematics, which are some good books for the domain of Operations research? I guess there are textbooks covering topics like linear and nonlinear optimization, convex optimization and quadratic programming, dynamic programming, multicriterial optimizations (did I miss something?)

Thanks,

Lucian

- Is there a unique saddle value for a convex/concave optimization?
- How to prove that $f$ is convex function if $f(\frac{x+y}2)\leq \frac12f(x) + \frac12f(y)$ and $f$ is continuous?
- Convexity of $\mathrm{trace}(S) + m^2\mathrm{trace}(S^{-2})$
- How to prove that the closed convex hull of a compact subset of a Banach space is compact?
- Segment ordered density conjecture revisited
- Why it is sufficient to show $|f'(z)-1|<1$?

- Prove that convex function on $$ is absolutely continuous
- in normed space hyperplane is closed iff functional associated with it is continuous
- Why are convex polyhedral cones closed?
- Pointwise supremum of a convex function collection
- closed epigraphs equivalence
- The distribution of barycentric coordinates
- Minimization of $\sum \frac{1}{n_k}\ln n_k >1 $ subject to $\sum \frac{1}{n_k}\simeq 1$
- Does every strongly convex function has a stationary point?
- Weakly convex functions are convex
- Relative interior of the sum of two convex sets

Stephen Boyd and Lieven Vandenberghe’s book is popular, and available free online:

http://www.stanford.edu/~boyd/cvxbook/

*Linear Programming* — *A Concise Introduction* by Thomas S. Ferguson and other ebooks/lecture notes on *Optimization* listed in Rod Carvalho’s web notebook.

Addendum: The classic and complete book by Hillier and Lieberman *Introduction to Operations Research*

If you want books that give a broad introduction to operations research (including optimization, queuing theory etc.)

The classics are:

**Operations Research – Ronald Rardin**

**Operations Research – Wayne Winston**

They are excellent from pedagogical point of view.

If you want to get into linear programming, this book is widely regarded to be one of the best:

**Linear Programming – Vasek Chvatal.**

For nonlinear programming:

**Nonlinear programming – Dimitri Bertsekas**

Here is a compilation of books taken from OR-Exchange.

http://industrialengineertools.blogspot.com/2010/08/favorite-operations-research-books-from.html

Winston-Operations Research-Applications and Algorithms is a very good book to start with.

introduction to operation research-**Hillier and Libermann**

They give pretty good motivation for the material being presented

This fits the bill: http://www.amazon.com/Understanding-Using-Linear-Programming-Universitext/dp/3540306978

J. Matousek even has an EMS prize (among others). Like T. Gowers.

Otherwise i also like the Boyd and Vandenberghe book suggested in another answer, but in my opinion that is not as lucid (has a much wider scope though ofc.).

Another remark about ‘Understanding and Using Linear Programming’ is that it is very easy – it is aimed at beginners. It’s not like number theory where almost any textbook claims to be an ‘introduction’ – this book means it.

Another obscure book with awful formatting that i like nonetheless is this http://books.google.de/books/about/Least_absolute_deviations.html?id=B1Q_AQAAIAAJ&redir_esc=y

- Sufficient conditions for an entire functions to be constant
- Explicit fractional linear transformations which rotate the Riemann sphere about the $x$-axis
- Full-rank condition for product of two matrices
- Is the group isomorphism $\exp(\alpha x)$ from the group $(\mathbb{R},+)$ to $(\mathbb{R}_{>0},\times)$ unique?
- A natural number multiplied by some integer results in a number with only ones and zeros
- How do I calculate this limit: $\lim\limits_{n\to\infty}1+\sqrt{2+\sqrt{3+\dotsb+\sqrtn}}$?
- Construction of a specific non-commutative and infinite group (with conditions on the order of the elements)
- Why does the median minimize $E(|X-c|)$?
- Help with a proof. Countable sets.
- Pullbacks of categories
- What type of curve is $\left|\dfrac{x}{a}\right|^{z} + \left|\dfrac{y}{b}\right|^{z} = 1$?
- Prove that if $f$ is a real continuous function such that $|f|\le 1$ then $|\int_{|z|=1} f(z)dz| \le 4$
- Prove that If $f$ is polynomial function of even degree $n$ with always $f\geq0$ then $f+f'+f''+\cdots+f^{(n)}\geq 0$.
- Finding a prime number $p$ and $x, y, z\in \mathbb N$ such that $x^p+y^p=p^z$
- The kernel and range of the powers of a self-adjoint operator