Questions tagged [oc.optimization-and-control]
Operations research, linear programming, control theory, systems theory, optimal control, game theory
1,214 questions
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Solving decoupleable families of FBSDEs
Let $d_1,d_2\in \mathbb{N}_+$, a stopping time $\tau$, and consider a system of BSDEs
\begin{align}
Y_{\tau}^1 & = \xi^1+\int_{t\wedge \tau}^{\tau}\, f_1(t,Y_t^1,Z_t^1,Y_t^2,Z_t^2)dt - \int_{t\...
- 4,822
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Monotonicity of the convex sum of two binary entropy functions
Let $T$ be some random variable on $[0,1]$, and define
\begin{equation}
\alpha(t) \triangleq \mathbb{E}[T \vert T\le t],\\
\beta(t) \triangleq \mathbb{E}[T \vert T>t], ~t\in[0,1].
\end{equation}
...
- 570
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Donsker-Varadhan duality in conditional sense?
A coherent risk measure named Entropic Value-at-Risk was introduced as follows: Let $(\Omega,\mathcal{F},\mathbf{P})$ be a probability space, $X$ be a random variable and $\beta$ be a positive ...
- 111
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Seeking Efficient Methods for Non-Convex Optimization Problem with Bilinear Term and Sparsity
I am working on a bilinear inverse problem arising in multi-channel signal processing. My problem background is to reconstruct a certain one-dimensional information $\mathbf{w} $ of an object from ...
- 1
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783
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A binomial optimisation problem
Consider a coin that comes up heads with probability $0 < p < \frac{1}{2}$. Fix some integer $N > 0$. We choose in advance a number of flips to run.
Write $H, T$ for the total number of heads ...
- 9,930
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57
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Comparision theorem for nonlinear integral Volterra equations with parameters
I am looking for comparision results for nonlinear integral Volterra equations with parameters. This was partially motivated by this paper. There, the author establishes, under mild hypothesis, the ...
- 1,465
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140
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Solving equations on a high dimensional torus
I want to establish some useful criteria for uniqueness of solutions to the following:
$$Mx=b,\\ \text{subject to}\ ||x(2k-1:2k)||=1, k=1,2,\cdots,5,$$ where $M\in\mathbb{R}^{10\times10},\ x\in\mathbb{...
- 81
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Softest transition from 0 to 1 on the real axis in minimum time
We want to get from 0 to 1 on the real axis with a moving point $P(x(t))$, that moves only in the right direction, as soft as possible in a minimum time. We introduce the class $\mathcal{S}$ ...
- 2,029
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118
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How is the derivative formula in equation (8) of the OptNet paper derived?
I'm studying the OptNet paper (Amos & Kolter, 2017), which integrates quadratic programs (QPs) into neural network layers and enables end-to-end learning through differentiable optimization.
In ...
- 101
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How to design encoders with the minimum number of rows?
Assume that matrices $\mathbf{A}$, $\mathbf{B}$, and $\mathbf{C}=\mathbf{A}\mathbf{B}$ are given. I aim to find matrices $\mathbf{E}_1$, $\mathbf{E}_2$, and $\mathbf{E}_3$ such that
\begin{align}
\...
- 199
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145
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Conjecture regarding the limit optimal transport under cost $\|x-y\|^p$ as $p\to 1^-$
Consider measures $\mu$ and $\nu$ in $\mathbb{R}^d$ with equal mass and no atoms, supported on a compact set, and make additional reasonable assumptions as necessary. Consider the optimal transport ...
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103
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How much can bounded volatility bias a martingale's moving-average exit?
Let $(W_t)_{t\ge 0}$ be a one-dimensional standard Brownian motion on its natural filtration $(\mathcal{F}_t)$.
For fixed constants
$$0 < \underline{\sigma} < \overline{\sigma} < \infty,$$
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62
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Details on the usage of projective transformations in Karmakar's algorithms
The question is related to this algorithm in linear optimization. In the algorithm, projective transformations are used as said by wikipedia:
Since the actual algorithm is rather complicated, ...
- 1,665
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219
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Optimization over loop spaces
I posted this question a few days ago to https://or.stackexchange.com/questions/13173/optimization-over-loop-spaces but didn't receive any replies, so I thought I would try here (if this is improper ...
- 4,131
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Variational problem of minimizing sum of Frobenius norms
I'm stumped by the following variational problem which came up in the course of my research. Let $X_1, X_2 \in \mathbb{R}^{m \times d}$ and $Y_1, Y_2 \in \mathbb{R}^{n \times d}$ be fixed matrices of ...
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