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

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

739
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### Minimize the asymptotic variance of an ergodic average subject to a set of constraints

Let
$(E,\mathcal E,\lambda)$ and $(E',\mathcal E',\lambda')$ be measure spaces
$f\in L^2(\lambda)$
$I$ be a finite nonempty set
$\varphi_i:E'\to E$ be $(\mathcal E',\mathcal E)$-measurable with $$\...

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17 views

### Canonical measure on Pareto front?

Suppose $F:\mathbb R^d\to\mathbb R^D$ encodes a set of objective functions on $\mathbb R^d$, and take $\mathcal S\subseteq \mathbb R^D$ to be the Pareto front of $F$. Under some genericity/smoothness ...

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77 views

+100

### Constrained iterative least square using Lagrange multipliers

I'm working on performing bundle adjustment of aerial images, and have finished the iterative unconstrained least squares part as follows
Calculating the design matrix (A), weights matrix (P) and ...

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55 views

### Approximate inverse of large sparse matrix

Given a large sparse matrix $M$, how to determine the existence of a good preconditioner? In other words, does there exist a sparse matrix $X$ such that $X M$ is close to the identity with respect to ...

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135 views

### Bounding the Frobenius norm of orthogonalised matrices

Context: I am trying to show the convergence of an optimization method which includes orthogonalization in the update step.
Problem: Let's say I have real matrices $A, B \in \mathcal{R}^{n xm}$. If ...

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144 views

### $0$-“norm” minimization with least-squares regularization

I have the following optimization problem in $\mathbf{x} \in \mathbb{R}^{K \times 1}$
$$\min_{\mathbf{x}>0} \quad \|\mathbf{A}\mathbf{x}\|_0 + \alpha \|\mathbf{B}\mathbf{x}-\mathbf{c}\|_2^2$$
...

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85 views

### Embedding a graph in $\mathbb{R}^3$ with partial geometric information

I have a connected, sparse, graph (a molecule to be specific) and I'm interested in associating 3D coordinates with the vertices. Here's the kicker: I already have coordinates for none/some/all ...

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18 views

### Existence of closed-loop stochastic control?

In a controlled system, for example,$dX_t=b(t,X_t,u_t)dt+\sigma(t,X_t,u_t)dW_t$, where $W_t$ is standard Brownian motion, $u_t$ is the controls strategies. If I want to find a kind of feed back ...

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22 views

### Convert the maximization problem with log objective function into exponential cone programming

Below is the problem definition and the detailed process I converted it into a formulation solvable by exponential cone solver. There are other constraints but for simplicity I omit them.
However my ...

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74 views

### KKT conditions for min-cost flow QP [closed]

I'm working on a convex quadratic separable min-cost flow problem with the following structure:
$P = \{\min \frac{1}{2}x^tQx + qx : Ex = b, 0 \leq x \leq u\}$
But I'm stuck on deriving the KKT ...

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60 views

### Unifying Optimal Control Problems through Constraint Optimization Problem

Consider Optimization problem in the form
$$\min ~ f(x) \quad \quad \text{subject to}\quad \quad F(x) \in C \subseteq Y $$
Where $F: X \to Y$ is continuously differentiable between banach spaces ...

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61 views

### Newton's minimizing method converge to local maximum [closed]

I have to minimize $f(x)=x^4-24x^2$ starting on the point $x_o=1$. The method converge to $x=0$, but i know that the solution is $x=+-2\sqrt{3}$. The hessian and the derivate of the function are $C_2$-...

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77 views

### Latent Dirichlet allocation and properties of digamma function

In the paper Blei, D. M., Ng, A. Y., & Jordan, M. I. (2003). Latent Dirichlet Allocation. Journal of Machine Learning Research, 3(4–5), 993–1022. http://www.jmlr.org/papers/volume3/blei03a/blei03a....

**1**

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70 views

### Shortest path on graphs

I would like to now if there has been any work on related problems, that is, shortest path problem in dynamically evolving graphs.

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56 views

### Lower semicontinuity of a multi-valued map $F:X\to 2^Y$ in term of net

Let $X,Y$ be two Hausdorff spaces and $F:X\to 2^Y$ be a multi-valued mapping. We says that $F$ is lower semicontinuous at $x_0\in X$ if for each $y_0\in F(x_0)$ and any neighborhood $U\in \mathcal N(...