# Questions tagged [decision-problems]

A decision problem is a question (in some formal system) whose answer is either "yes" or "no".

8 questions
1answer
43 views

### Nonempty interior is equivalent to the feasibility of set of strict quadratic inequalities. Why?

From Convex Optimization: Let $E_i = \{x \mid f_i(x) \le 0\}$ where $f_i(x) = x^TA_ix + 2b_i^Tx + c_i$ for $i = 1, 2, \dots, m$ and $A_i \in S^n_{++}$ where $S^n_{++}$ is the set of all ...
0answers
41 views

### How to quickly determine if a linear program is feasible?

I have a series of linear programs in canonical form $$\begin{array}{ll} \text{maximize} & c^T \mathrm x\\ \text{subject to} & A x \leq b\\ & x \geq 0\end{array}$$ and I need to ...
0answers
483 views

### Determine if a polyhedron is a polytope

Note, a polyhedron is the intersection of finitely many half spaces in $\mathbb{R}^n$ and a polytope is a bounded polyhedron. Let $M$ be an $m \times n$ matrix of integers. Let $P$ be the (possibly ...
0answers
28 views