# Tagged Questions

Operations research, linear programming, control theory, systems theory, optimal control, game theory

46 views

### About the critical points of quasi-convex functions

What do we know about the structure of critical points of quasi-convex functions? I am looking for statements like "the critical points of a quasi-convex function are always either a global minima ...
42 views

14 views

### Under which conditions discretization of convex\concave function is submodular?

Say, I have $f(x)$ with $x \in [0,1]$, then by discretization I mean $f(x_h)$ with $x_h \in \{0, h, 2h, \dots, 1\}$. I know about Lovasz extension, but it works in other way: given discrete function ...
126 views

### Orthogonal Procrustes problem with Absolute Values

Given a non-negative matrix $T$, how to find a orthogonal matrix $O$ minimising $$\left\lVert \, |O| - T \right\lVert_F,$$ where $\lVert \cdot \lVert_F$ denotes the Frobenius norm, and $| \cdot |$ ...
38 views

### optimize a Quadratic Matrix Programming with multi-spherical constraints

I have got the following quadratic problem restricted on the Cartesian product of Euclidean spheres. $\underset{X \in \mathbb{R}^{n\times 3}}{\text{min}}$ $Q(X) = \frac{1}{2} Tr(X^TA X) + Tr(B^T X)$ ...
422 views

### Supremum in a Markov chain model

A Markov chain $X$ with finite state space $\{1,2,\cdots,N\}$ is defined on a probability space $(\Omega, P, \mathcal{F})$ equiped with filtration $\{\mathcal{F}_t\}$. And we assume that we can reach ...
99 views

### Fixed point iteration on symmetric biconvex function

Suppose $X\subseteq\mathbb{R}^n$ is a convex set and that a function $g(x,y):X\times X\rightarrow\mathbb{R}_+$ is smooth, "strictly biconvex" (strictly convex in $x$ and $y$ independently but not ...
85 views

270 views

### An inequality on the simplex involving $x^x$

Is anything known about the behavior of the function $$f(x)=\prod_{i=1}^n x_i^{x_i}$$ on the standard simplex, i.e. the set $\{x\in\mathbb{R}^n:\sum_{i=1}^n x_i=1, x_i\geq0\}$? I ask because I have ...
350 views

### Euler-Lagrange equations and Bellman's principle of optimality

One method to optimize the integral $$\int_{\mathcal T} L(t,x,\dot{x}) \; dt$$ of a functional over a curve is the calculus of variations, which leads to ordinary differential equations: the Euler-...
72 views

### The state-transition-matrix of a physical system,

Here's a simple but potential research problem that I am learning about. Let's say I am studying a physical system that is governed by N objects. At each time, each object is either "active" and ...
32 views

### computational-expensive signal reconstruct - a combination problem [closed]

My problem is: I have a time series signal (vibration signal), use BSS algorithm (Blind Source Separation, we can regard it as a black box), separate the source signal into 100 components. Now I ...
177 views

### Max Absolute Difference of Expectations under Change of Measure

Given a sample space $\Omega=\{ 1,\cdots,N \}$, a random variable $x$ defined on $\Omega$ that takes value $x_1,\cdots,x_N$, and a set of strictly positive real numbers $w_1,\cdots,w_N$. Define for ...
68 views

### Optimization with vectors

I am trying to solve the following optimization problem as a small part of a research project, and I do not know if there exists closed form solutions. My linear algebra is very rusty and I am looking ...
193 views

### Covering max flow arcs by arc disjoint paths

Let $(N,A,s,t,u)$ be a network with node set $N$, arc set $A$, source $s\in N$, sink $t\in N$ and capacity vector $u\in\{1,2,\ldots,T\}^A$, and let $x=(x_a)_{a\in A}$ be a maximum $(s,t)$-flow. Is it ...