# Questions tagged [oc.optimization-and-control]

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

**0**

votes

**0**answers

15 views

### Can the partial concavity of the following decomposable objective function be used for optimization?

The problem I am trying to solve is the following:
$$\begin{array}{ll}
\min & f(x)+g(y) \\
\mathrm{s.t.} & y\ge x\ge 0,\\
\ & p\le ax+by\le q,
\end{array}$$
where $a,b,p,q$ are ...

**1**

vote

**1**answer

36 views

### Measuring how suboptimal control is

Suppose I have a linear dynamical system to control. I use PMP to find necessary conditions for the optimal control of the system wrt to some objective function. Now, suppose that the trajectory I ...

**5**

votes

**0**answers

108 views

### Rigorous proof of the good regulator theorem

As an applied mathematician with an interest in control theory, I have read several research papers that explicitly use the good regulator theorem of Conant and Ashby 1 which states that:
Every ...

**1**

vote

**0**answers

13 views

### Simple examples of the Chen–Fliess series and the Fliess operator applications

I am looking for simple examples of the application of the Chen–Fliess series to input–output systems.
In the best case scenario, something like linear systems affine in control for which the result ...

**3**

votes

**1**answer

182 views

### Best approximation of a compactly supported density by a single Gaussian

Note: This is a follow-up question inspired by a previous (more difficult) question I asked on MathOverflow.
Let $f:\mathbb{R}\to\mathbb{R}$ be a (sufficiently regular, e.g. smooth) probability ...

**0**

votes

**1**answer

61 views

### Conditioning on an irrelevant variable in a martingale control problem

Suppose I have two independent Brownian motions $B^1_t, B^2_t$ and $\mathbb F_t$ be the natural filtration generated by them. Let $T > 0$ be a fixed finite number. Let $q_t$ be a $[-1,1]$ valued $\...

**1**

vote

**1**answer

112 views

### Trajectory leaving a set

Consider the differential equation $\dot{x}=f(x)$, where $f: \mathbb{R}^2 \to \mathbb{R}^2$ is smooth. Given a set $A \subset \mathbb{R}^2$, are there some results saying that whenever $x(0) \in A$, ...

**3**

votes

**2**answers

82 views

### Expected minimum of a linear function on the unit cube

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\...

**0**

votes

**0**answers

33 views

### Convex optimization problem with really simple submodular structure

I am trying to characterize the solutions to the below convex optimization problem as concisely as possible, where we are given as input a probability vector $\mathbf{p}\in\mathbb{R}^n$ and a positive ...

**1**

vote

**0**answers

21 views

### Optimal control problem with spike source and “split” state

For $p \in \mathbb{R}$, consider the following problem:
\begin{equation} \label{1}
\begin{cases}
\operatorname{div}(a \nabla u ) = p\delta_{x_0} \quad \text{in } \Omega \\
u=0 \quad \text{on } \...

**3**

votes

**0**answers

161 views

### Equal principal minors of matrix plus rank-1 and inverse

Given an invertible real matrix $A$ and real column vectors $b$ and $c$.
For which $A$, $b$ and $c$ are all corresponding principal minors of $B = A-bc^T$ and
$A^{-1}$ equal?
According to a ...

**6**

votes

**0**answers

237 views

### Geometric bang-bang theorem for nonlinear optimal control

The classical bang-bang theorem is usually stated for linear systems (e.g. Control Theory from the Geometric Viewpoint by Agrachev-Sachkov, p. 209). Sussman proved a nice generalization for systems ...

**0**

votes

**0**answers

30 views

### Single step analysis of Augmented Lagrangian Method

I am wondering if there is any single step analysis for the Augmented Lagrangian method. Specifically, the problem is
$$\min f(x) \text { s.t. } A x=b$$
where $f$ is convex, smooth. Such an objective ...

**5**

votes

**0**answers

117 views

### How to choose phase to give a desired Fourier transform

Cross posted from MSE.
I have a mathematical problem arising from a physics application, which I feel must have been solved before, but I don't know the terminology associated with it. I am looking ...

**0**

votes

**0**answers

14 views

### Parametric research for the global minimum in a family of polynomial multivariable functions on closed domains

Consider the family of functions:
$$
V(\{x_j\},\{y_j\})=\sum_{j=1}^L\left[\frac{1}{2} x_j^2+ \frac{\beta^2}{2}y_j^2 + \alpha\beta\, x_jy_j \right]
$$
Each member of the family is therefore ...