# Tagged Questions

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

22 views

### Covering Number of a Positive Semidefinite Cone (Approximate the Objective of a SDP)

I was wondering what the covering number of a positive semidefinite cone is. Consider the semidefinite optimization program \begin{align} \max\langle \mathbf{C}, \mathbf{X} \rangle~~\text{subject to}~...
47 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 ...
43 views

73 views

### Optimal control / Portoflio optimization: Maximize expected utility of total consumption

I came across a portoflio optimization problem, where I need to solve for optimal investment and consumption processes, such that the expected utility of total consumption and terminal wealth is ...
94 views

### Finding the right σ-algebra. Question on uncertainty related to the secretary problem

Assume a number of iid. items is presented and the task was to stop under the objective of picking the best item. In this setting it is relevant what is the distribution of the values of the ...
34 views

### Edge-disjoint paths avoiding some subgraphs

Let $G$ be a directed graph on $n$ vertices. Let $H_1$, ..., $H_k$ be marked subgraphs of $G$. (Specifically, each $H_i$ consists of a subset of the vertices of $G$ and a subset of the edges of the ...
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 ...
74 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 ...
37 views

138 views

### Global minimum of nonlinear least square

We have a continuous and differentiable function $f(\cdot)$ that maps from $R^n$ to $R^n$. We are trying to solve a nonlinear least square problem: Minimize $J(x)=\Vert f(x)-z\Vert^2$ subject to box ...
129 views

Let $\Pi$ denote the space of all permutations of $\{1,\dots,n\}$, and let $d(\cdot,\cdot)$ be a metric on $\Pi$. Suppose I am given a large integer $K$ and I have to select $K$ permutations $\pi_1,\... 0answers 52 views ### Separable Least squares - is there a notion of conjugate directions? I have a general question. Suppose I have the following to optimize $$\|Y-A(\mathbf{x})B(\mathbf{y})\|^2$$ where$Y$is a vector,$A(\mathbf{x})$is a matrix that depends on a vector$\mathbf{x}$in a ... 1answer 45 views ### On optimizing a function whose projection and projected vector go through a linear transformation Assume the two sets of vectors$\{\mathbf{a}_1,\ldots,\mathbf{a}_N\}$and$\{\mathbf{b}_1,\ldots,\mathbf{b}_N\}$of equal length. My goal is to find the optimum matrix$\mathbf{C}$to the following ... 0answers 29 views ### Maximisation of a discrete linear function I am trying to maximise the function $$Q=\sum_i{\alpha _{i}x_{i}}$$ subject to the constraint $$W<=\sum_i{\alpha _{i}w_{i}x_{i}}$$ By changing$\alpha _{i}$subject to$ 0<=\alpha _{i}<=1$... 0answers 65 views ### Curves in$\mathfrak{su}(n)$with specific property Consider a curve$\gamma_s= U_s^{\dagger} b U_s$in$\mathfrak{su}(n)$where$U_s$is a smooth curve on$SU(n)$(starting at$U_0 = \mathbb{I}$) and nonzero$b\in \mathfrak{su}(n)$and$s \in[0,T]$... 0answers 27 views ### Equivalence between multiclass SVMs, power diagrams, and constrained$k$-means Apologies in advance for the long post: Suppose we have a collection of points$\mathbf{p}_1,\dots,\mathbf{p}_n$in$\mathbb{R}^d$, and we consider the following three ways of partitioning these ... 2answers 291 views ### More general than semidefinite program? I was TAing my convex optimization class and explaining that Linear Programs are a special case of Second Order Cone Programs, which are themselves special cases of Semidefinite Programs. My question ... 1answer 301 views ### Kalman filters and stock price prediction Could someone be so kind as to direct me to a good source that would explain time series (more specifically) stock price prediction using Kalman filters, Extended kalman filters or particle filters. ... 0answers 93 views ### approximation of rational functions Suppose$\hat{p}/\hat{q}$and$p/q$are two rational functions where$p,q,\hat{p},\hat{q}$are of degree$n$. Suppose they satisfy that$|p(z)/q(z) - \hat{p}(z)/\hat{q}(z)| < \epsilon$for any$z$... 1answer 101 views ### Is the linear production game a convex game? In cooperative game theory, the linear production game (LPG) is defined by letting the characteristic function have the form of a linear programming problem. Does anyone know if the LPG is a convex ... 0answers 19 views ### Can MDPs over functions be solved? I understand that dynamic programs are difficult to be solved in general. However I have an MDP, for which intuitively I have a solution, I am curious to know if there is a formal approach to get a ... 0answers 48 views ### Applications of systems with multiple time A dynamical system with multiple time is an action of a group$\mathbb{Z}^d$or$\mathbb{R}^d$on a metric space. I am interested in informative examples and applications of such systems. I know ... 0answers 21 views ### Deterministic global solution to find the Optimal-knot placements for continuous piecewise linear functions to fit nonlinear data I have been searching lately for a deterministic global technique to linearize a nonlinear function with continuous piecewise linear regions. I've a univariate nonlinear function y=f(x). where f(x) ... 0answers 52 views ### Is there a name for this variant of the MST and the TSP? Suppose I am given a weighted graph$G$that contains a "start vertex"$v_0$, and my goal is to construct a set of paths that all originate at$v_0$and touch all of the vertices of$G$, with as ... 0answers 21 views ### Bounding the error of the optimal solution from an approximated objective Let$f$be a smooth convex function defined in a bounded region$X$and its Hessian is bounded$m I \le |\frac{\partial^2 f(x)}{\partial x^2}| \le M I$for some$M>m>0$. Let$x^*=argmin_{x\in X} ...
Given a control system on $\mathrm{SU}(n)$ (or any other compact, semi-simple Lie group I suspect) of the form: $\frac{d U_t}{dt} = (A + w(t)B)U_t$ where $A,B \in \mathfrak{su}(n)$ generate the ...