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I am trying to solve an unconstrained optimization problem with the following properties: I am given a graph $G=(V,E)$ with functions $f_{ij}:\mathbb{R}^2\to \mathbb{R}$ for each edge $(i,j)$. I am tr …

Let $c\in\mathbb{R}^n$ and let $X_1,X_2$ be two independent uniform samples on the unit cube in $\mathbb{R}^n$. Is there anything at all (in an analytic sense) we can say about the expectation $E\min …

Let $S \subset \mathbb{R}^n$ satisfy $0\leq x_1\leq\dots\leq x_n$ for all $\mathbf{x}\in S$, among other (possibly nonconvex) constraints, and suppose in addition that $\sum_{i=1}^n x_i \geq 1$ for al …

Consider a standard linear program of the form $$\textrm{minimize}_x~~~~ c^Tx~~~~ s.t. \\ Ax = b \\ x \geq 0$$ with $x\in \mathbb{R}^n$ and $A \in \mathbb{R}^{m \times n}$. It is well known that, if …

Can anyone direct me to any algorithms or theorems that describe the difficulty of solving a non-smooth convex optimization problem for the special case where the full subdifferential is available? A …

Is there a commonly-accepted umbrella term for infinite-dimensional calculus problems where the goal is to compute an optimal geometric path between a pair of points? Three examples of this would be …

This is not a homework problem, although I fear it may turn out to be at that level. For any nonnegative $x\in\mathbb{R}^n$, let $f_k(x)$ be the sum of the $k$ largest values in $x$, and define $$f(x …

The max flow-min cut theorem is one of the most famous theorems of discrete optimization, although it is very straightforward to prove using duality theory from linear programming. Are there any othe …

Let $X$ be a subset of $\mathbb{R}^d$, let $\|\cdot \|_p$ be a norm with $1\leq p\leq\infty$, and let $f:\mathbb{R}^d\to\mathbb{R}$ be a function. I'm trying to find examples of $X$, $p$, and $f$ for …

I am struggling with a fairly simple and natural geometric optimization problem, but I have not been able to find an obvious canonical method for solving it: I am given a collection of $m$ axis-align …

Can anyone point me to an example of a problem that (more or less) originated in computational geometry whose solution requires the use of Lagrange multipliers (or Kuhn-Tucker conditions, or dual vari …

Suppose I am given $n$ points $p_1,\dots,p_n\in \mathbb{R}^2$, as well as two positive coefficients $a_1$ and $a_2$, and I am trying to select $n$ points $x_1,\dots,x_n$ to solve the following optimiz …

Given a path $P$ in the unit square, and two points $p_{1},p_{2}$ located on $P$, let $d_{P}(p_{1},p_{2})$ denote the distance from $p_{1}$ to $p_{2}$ traversed along $P$. Given $a>1$, I am looking f …

Suppose I have a convex polygon $C$ and a radius $r>0$, and I seek a path $P$ that "covers" $C$, in the sense that any point $C$ is within distance $r$ of $P$: $$d(x,P)\leq r~\forall x\in C~,$$ where …

If I sample a large number of uniform points in the unit square and take a traveling salesman tour of them, is there anything at all that can be said/is known about the distribution of angles at each …