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# Questions tagged [convex-hull]

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### Non-convex optimization with correlated minima

I am thinking of non-convex optimization problems where the minima are somehow correlated. Maybe there are symmetry relationships among minima or maybe there is regularity in spacing among minima in ...
• 651
1 vote
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### Detailed exposition for proof of Localization Lemma in paper "Random Walks in a Convex Body and an Improved Volume Algorithm"

I've begun reading the paper "Random Walks in a Convex Body and an Improved Volume Algorithm" by Lovász-Simonovits ('93). Although the paper for the most part is pretty self-contained and ...
112 views

### Strongly polynomial time algorithm for shortest convex combination

Problem: Let $S$ be a finite set of vectors. Let $C$ be their convex hull. Compute $\operatorname{argmin}_{x \in C} \|x\|$. Reference 1 gives an algorithm for this problem that is finite-time (Section ...
• 662
1 vote
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### How to enforce convexity?

I have a problem for which the solution is known to be a convex $f:[a,b]\times[c,d] \rightarrow \mathbb{R}$ over some rectangular domain ($a<b$ and $c<d$). There are many situations (e.g. ...
• 111
195 views

### Restriction of a convex function to {0, 1}^n

Suppose I have a real-valued convex function $f$ on the unit hypercube $[0,1]^n$, and let $\bar{f}$ be its restriction to the integer points $\{0,1\}^n$. Does $\bar{f}$ satisfy any properties, or can ...
• 43
228 views

### Convex polygons inclusion relation

I have the following problem which came as a subproblem in some work I was doing and I am completely stuck. Note that I am interested in it only in terms of worst case time complexity (not heuristics ...
• 41
1 vote
17 views

• 1,095
1 vote
88 views

### Convex hull of codebook (LP-decoding)

So the well-cited article by Feldman et al from 2005 has a method of constructing the convex hull of the feasible set for ML-decoding. Basically, he considers the parity check matrix $H$ as a Tanner ...
• 263
267 views

### When can a convex function induce submodularity?

Say I have a real valued convex function $f$ on the hypercube $[-1,1]^n$. Let $f'$ be the induced function on the discrete hypercube $\{-1,1\}^n$. Now I want to find a vertex on $\{-1,1\}^n$ on which ...
• 654
1 vote
I am new to computational geometry so pardon me for the lack of formalism. I am currently experimenting with an algorithm of mine in which I need to extend recursively a Delaunay graph in $d$-space. ...
Consider the convex hull problem in $\Re^d$: Input: a list of $n$ points $S$ in $\Re^d$, Output: the vertices of the convex hull of $S$. What is the best lower bound on the time complexity of ...