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Search options user 3200
6
votes
0answers
Let $$A \cdot X + B \preceq 0$$ be a system of linear inequalities with $X \in \mathbb{R}^n$ $A\in \mathbb{R}^{m\times n}$ and $B \in \mathbb{R}^m$ where $m \geq n$. According to Farkas lemma, exactly …
asked Oct 26 '20 by C Marius
2
votes
3answers
Let $\mathcal{U} = \{ [x_1, ..., x_n] \in \mathbb{R}^n : 0 \leq x_i \leq 1\}$ be the unit hypercube and $C \in \mathbb{R}^n\setminus\mathcal{U}$ fixed. Let us consider the following problem $$ \max_{X …
asked Dec 2 '20 by C Marius
7
votes
1answer
Let us assume that an optimization algorithm requires $\mathcal{O}(n^{\log1/\epsilon})$ flops to find a solution $\bar{X}$ such that $$\| \bar{X} - X^{\star}\| \leq \epsilon$$ where $\epsilon < 1$ a …
asked Apr 15 '20 by C Marius
6
votes
2answers
Given two ellipsoids \begin{align}\mathcal{E}_1 &= \{ X \mid X^\top A_1 X + 2B_1^\top X + C_1 \leq 0\}\\\mathcal{E}_2 &= \{ X \mid X^\top A_2 X + 2 B_2^\top X + C_2 \leq 0\}\end{align} are both non-em …
asked Apr 21 '20 by C Marius
4
votes
1answer
Problem description Let $\mathcal{C} = \{X \in \mathbb{R}^n \mid g(X) \leq 0\}$ with $g(X)$ a convex function. Suppose I need to solve the feasibility problem, for a given $r>0$ $$ \exists ^?X \in \ …
asked Mar 25 '20 by C Marius
3
votes
1answer
For $f : \mathbb{R}^{n \times 1} \to \mathbb{R}$ a double differentiable function with bounded hessian, not necessarily convex, is any known polynomial algorithm, in the general case, which can assert …
asked May 25 '21 by C Marius
9
votes
1answer
Problem Let $\mathcal C = \{ X \in \mathbb{R}^n \mid g(X) \leq 0\}$ where $g$ is convex, and let $X_c \in \mathcal{C}$. Is there any algorithm to compute the distance from $X_c$ to the boundary of $\ …
asked Mar 17 '20 by C Marius