Questions tagged [nonlinear-optimization]
Nonlinear objectives, nonlinear constraints, non-convex objective, non-convex feasible region.
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Numerical implemenation of denoising data using maximum entropy
I am trying to reproduce a denoising approach from a paper titled "Near-optimal smoothing using a maximum entropy criterion" (Link). This paper is from 1992 and also checked the PhD thesis ...
- 791
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Minimizing a Function with Nonlinear Constraints
I am trying to minimize the function $f(x, y) = \frac{1}{x} + \frac{1}{y}$ subject to the constraints:
$$
x + \frac{x}{x + y} y - c \leq 0,
$$
$$
x \geq 0,
$$
$$
y \geq 0.
$$
I have attempted to use ...
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A maximisation problem : finite or not?
Let $\mathcal M_2$ be the space of real $2\times 2$ matrices and $\mathcal S_2\subset \mathcal M_2$ be its subset consisting of positive semidefinite elements, i.e. $A\in \mathcal S_2$ iff $A$ is ...
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Extension of this maximisation problem : finite or not?
$\mathcal M$ is the space of real $d\times d$ matrices and $\mathcal S\subset \mathcal M$ is its subset consisting of positive semidefinite elements. We consider the distance the product space $\...
- 1,111
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$k$-subset with minimal Hausdorff distance to the whole set
Let $(\mathcal{M}, d)$ be a metric space. Let $k \in \mathbb{N}$. Let $[\mathcal{M}]^k$ be the set of $k$-subsets of $\mathcal{M}$. Consider the following problem:
$$ \operatorname*{argmin}_{\mathcal{...
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1
answer
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views
Does this maximisation problem admit a finite upper bound?
Let $\mathcal M_2$ be the space of real $2\times 2$ matrices and $\mathcal S_2\subset \mathcal M_2$ be its subset consisting of positive semidefinite elements, i.e. $A\in \mathcal S_2$ iff $A$ is ...
- 1,111
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How to formulate piecewise quadratic function optimization without introducing binary variables?
I have a problem with logical constraints (either-or constraints). I know that it can be solved by either big-M or complementary formulations. However, i do not want to convert it into mixed-integer ...
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Minimizing the Spectral Norm of the Hadamard Product of a Quadratic Form Using CVX
I am trying to use CVX to minimize the spectral norm of the Hadamard product of two matrices, one of which is in quadratic form. Specifically, I am trying to minimize $\|{\bf A} \odot {\bf XX}^H\|_2$, ...
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How to prove the convergence of Gechberg-Saxton algorithm?
I just have a problem that Gerchberg-Saxton algortihm is no worse than the previous iteration
but not sure whether it is convergent.
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answer
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Equivalence of minimizing trace and determinant over matrix quadratic form in multivariate regression
Consider the multivariate regression model
$$Y = XB + E$$
where $Y$ is $n \times p$ and corresponds to the dependent variables, $X$ is $n \times k$ and corresponds to the independent variables, $B$ is ...
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Gradient descent over the set of complex symmetric matrices
In the course of my research (somewhat related to compressive sensing), I am trying to determine a complex, symmetric matrix $L$ (i.e. $L = L^T$) through the following optimization formulation:
$$ \...
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answer
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Clarification about this optimisation problem
Good morning everybody. First of all, I apologise to ask here the same question I asked on MSE three days ago, but I am in fact re-asking since I obtained no relevant advice. Perhaps I will hear some ...
- 149
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Generalizations of Berge's maximum theorem
I have a parameterized optimization problem
\begin{eqnarray}
\max_{x\in D(\theta)} f(x,\theta).
\end{eqnarray}
Assumptions of the standard Berge's maximum theorem are satisfied, so the value function $...
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How can we calculate the Euler-lagrange equations?
In this paper https://arxiv.org/pdf/1907.09605.pdf \
let $\Omega \subset \mathbb{R}^n$ with $n \geq 1$ be a bounded Lipschitz domain with boundary $\partial \Omega$, $f: \Omega \rightarrow \mathbb{R}$ ...
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Under which condition, such that all second-order critical points satisfy $\sum_j\cos(\theta_i-\theta_j)>0$ for all $i\in[n]$?
Consider the following non-convex function
$$E(\theta):=-\sum_{i,j}A_{ij}\cos(\theta_i-\theta_j)$$
where $A$ is a symmetric, diagonal-free matrix whose non-diagonal element are $\pm 1$. In other words,...
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