All Questions
9 questions
1
vote
1
answer
309
views
Numerical estimation of partial derivatives of convolved functions when closed forms do not exist
Summary: Some peak functions are convolutions which may not have a closed form solution. A classical example can that of a Voigt which is a convolution of a Lorentzian and a Gaussian, followed by ...
- 879
3
votes
1
answer
158
views
Numerical scheme for convex optimization
Given $(e_n)_{-N\le n\le N}\in\mathbb R^{2N+1}$ and $-1<x<1$, solve
\begin{eqnarray}
&&\max_{(q_n)_{-N\le n\le N}\in\mathbb R^{2N+1}_+}~ \sum_{n=-N}^N (e_n-\log(q_n))q_n \\
\mbox{s.t.} &...
user128095
2
votes
0
answers
40
views
Numerical algorithms for geodesically convex optimization
I want to solve a minimization problem of the form
$\inf_{x \in M} f(x)$
where $M$ is a Hadamard manifold and $f$ is geodesically convex (but not differentiable). Since I know that in general a ...
user85365
0
votes
0
answers
68
views
Numerically solve a specific saddle-point problem
Let $(\Omega,\mathcal E,\mu)$ be a probability space, $k\in\mathbb N$, $$W:=\left\{w:E\to[0,\infty)^k:\sum_{i=1}^kw_i=1\;\mu\text{-almost surely}\right\},$$ $G$ be a finite nonempty set and $a^{(g)}:E\...
- 167
1
vote
0
answers
79
views
Minimization of a smooth integral functional over a closed convex set
Let $(E,\mathcal E,\mu)$ be a probability space, $I$ be a finite nonempty set, $\gamma:(E\times I)^2\to[0,\infty)$ be measurable, $$F_1(g,w):=\sum_{i\in I}\int\mu({\rm d}x)w_i(x)g(x)\sum_{j\in I}\int\...
- 167
2
votes
2
answers
323
views
Reference request on computational schemes for $\inf_{x\in\Omega^n}\sup_{y\in\mathbb R^n}F(x,y)$
Let $\Omega\subset \mathbb R^d$ be compact, $\rho$ be a density function on $\Omega$ and $p_1,\ldots, p_n\in (0,1)$ be weights satisfying $\int_{\Omega}\rho(z)dz=1=\sum_{k=1}^n p_k$. We consider the ...
user128095
1
vote
1
answer
1k
views
On solution methods for min-min optimization problems
Closely related (although not equivalent) to minimax optimization problems is the following:
$$\min_{x \in \Omega} \min_{i=1,...,q} f_i (x).$$ Here, $\Omega \subset \Bbb R^n$ and $f_i: \Bbb R^n \to \...
- 185
2
votes
0
answers
88
views
Gradient Descent with derivative constraints
tl;dr: I need bound results for the derivative of some big honking function.
tfa: I am trying to solve an optimization problem:
Find a parameter vector $\theta$ so that $\sum_x \log f(\theta, x) \...
- 245
3
votes
2
answers
266
views
Fixed point iteration on symmetric biconvex function
Suppose $X\subseteq\mathbb{R}^n$ is a convex set and that a function $g(x,y):X\times X\rightarrow\mathbb{R}_+$ is smooth, "strictly biconvex" (strictly convex in $x$ and $y$ independently but not ...
- 705