Questions tagged [convex-optimization]
Optimization with convex constraints and convex objectives; notions related to convex optimization such as sub-gradients, normal cones, separating hyperplanes
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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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How to deal with minimizing a flat objective function
Problematic (Debiased Sinkhorn barycenter, proposed by H.Janti et al.): Let $\alpha_1, \ldots, \alpha_K \in \Delta_n$ and $\mathbf{K}=e^{-\frac{\mathrm{C}}{\varepsilon}}$. Let $\pi$ denote a sequence ...
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When are infimal convolutions contractions?
Let $X$ be a separable Fréchet space and $\varphi,\psi:X\to \mathbb{R}$ be a lower semi-continuous and convex function with $\psi$ bounded below and coercive. Consider the infimal convolution
$$
\...
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How explicit the optimiser of this optimisation problem can be?
Provided the given parameters as follows :
$\mu\in\mathbb R, \sigma\in\mathbb R_+$ are constant, $\kappa, r, \alpha, \beta: \mathbb R_+\to\mathbb R_+ $ are measurable functions such that $\kappa(y)\...
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Separating domains in $\mathbb{R}^{2n}$ by a real algebraic variety
Suppose $\Omega_1$ and $\Omega_2$ are two disjoint unbounded domains in $\mathbb{R}^{2n}$, $n \in \mathbb{N}$. Can there be conditions on $\Omega_1$ and $\Omega_2$ so that these two domains can be ...
- 171
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Software for computing polytopes
As can be inferred from the title, I want to do some computation on the facets representation of the polytopes given the vertices. My advisor recommended me Polymake, which is indeed useful even with ...
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Stopping criteria for damped Newton iterations with backtracking line search
Are there better criteria than the Armijo criterion for damped Newton iteration with backtracking line search, when the objective is standard self-concordant? (See Boyd and Vandenberghe.)
Let $F(x)$ ...
- 897
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Touring a sequence of convex polygons with minimal energy
There is a known problem of touring a sequence of $n$ polygons: given a starting point $s$, an ending point $t$ and a sequence of polygons $P_1,\dots,P_k$ with a total of $n$ vertices, find points $...
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Convex optimization of the Lovász extension of a submodular function
I have a finite set of $n$ elements $A$, and a submodular function $f:2^A\rightarrow R$.
Let $g:[0,1]^n\rightarrow {R} $ be the Lovász extension of $f$.
I want to solve the following optimization ...
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Efficient counting of integer solutions to linear system
In my research, I have a particular 18x18 matrix $\mathbf{A}$ which defines the linear system $\mathbf{A}\cdot \mathbf{x} \leq \mathbf{-1}$ over the nonnegative integers. And I'm interested in ...
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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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Strengthening the Kovner-Besicovich theorem: Does every unit-area convex set in the plane contain a centrally symmetric hexagon of area $2/3$?
The Kovner-Besicovich theorem states that every convex set $S$ in the plane contains a centrally symmetric subset $C$ of at least $2/3$ the area of $S$, and that this bound is sharp for triangular $S$....
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Approximate local minima for sum of inverse trigonometric functions
Let $\{a_1, a_2, ..., a_N\} \in [0, 1[^N$, I would like to approximate the minimum of the function
$$f(x) = x \sum_{i=1}^N \left(\sin(x)^2 - \sin(a_i x)^2 \right)^{-2} $$
in the domain $x \in {]0, \...
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Equivalence of minimizing trace and determinant over matrix quadratic form in multivariate regression
Consider the multivariate regression model
$$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 ...
