There is an enormous amount of information about the common applied math problem of minimizing a function.. software packages, hundreds of books, research, etc. But I still have no …

Suppose that a parent brings home from a trip $2n$ gifts of roughly equal value for his/her two children. The children get to choose one at a time which gifts they want. What is th …

Let us consider a probability distribution $(g_n)_{n \in \mathbb{N}}$ which we want to approximate by a mixture of $(f_n(\lambda))_{n \in \mathbb{N}}$ where $\lambda \in \mathbb{R} …

I'm interested in the solution to the following problem: I have initial capital $C$ which I can invest into $M$ classes of resources, each unit of a class $m_i$ matures at time $t …

Suppose there are $ K $ buckets each can be filled upto $ N-1 $ balls. The gain on putting $ i $ balls in the $ k^{th} $ bucket is given by $ \Delta l_{k,i}, \, i \in [1,N-1] $. …

I'm probably missing something elementary here, but I guess the only way to be sure is to ask here. Now, I have encountered a situation where given an nth-degree polynomial $p_n(z …

Are there results that bound the asymmetry of the duality gap of an integer program? That is to say, if the difference between the LP solution and the IP (primal) solution is $a$, …

I'm trying to solve the following least squares problem: $\underset{x}{\text{min}} ||Ax - \tilde{b}||_2$ where $Ax = b$ and $\tilde{b} = b + w$ Question: How do I determine whi …

You notice a stop-light ahead of you and it is currently red. You can't run the red light, so you will have to brake, but braking wastes energy and you want to be as fuel efficien …

Convex Optimization is a mathematically rigorous and well-studied field. In linear programming a whole host of tractable methods give your global optimums in lightning fast times. …

Let $Q$ be an $n \times n$ real symmetric matrix and $x$ an $n \times 1$ real vector. Consider the following minimization problem: $\min_{\pi \in S_n} ~(\pi x)^{\rm T} Q (\pi x)$ …

The reason I am wondering this is that all of the reductions from 3-SAT => quadratic programming (or similar NP-hard reductions) involve encoding the underlying NP-hard problem int …

The Littlewood-Richardson cone $LR_{n, k}$ consists of all $k-$tuples $(a_1, a_2, \dots, a_k)$ of real $n-$vectors with monotonically decreasing entries such that there exist $k$ $ …

I'm trying to solve the BVLS problem for huge (2e6x2e6) matrices which are very sparse (4 elements per row). Does anybody have a recommendation for a free solver (preferably a libr …

There is a linear function of two variables that I am trying to minimize under an equality constraint. But, the constraint is non linear in the variables. Is there any technique to …