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Results tagged with convex-optimization
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user 172374
Optimization with convex constraints and convex objectives; notions related to convex optimization such as sub-gradients, normal cones, separating hyperplanes
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Establishing quasiconcavity
I will provide a criterion under which certain sums preserve quasiconcavity. Since it is not covered in traditional convex optimization textbooks ala Boyd & Vandenberghe (2004), since it is quite rece …
- 67
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2
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Establishing quasiconcavity
Let $f:\mathbb{R}_+\rightarrow\mathbb{R}_+$ be twice differentiable quasi-concave function satisfying $f(x)>0,\forall x \in \mathbb{R}_+$. Let $g:\mathbb{R}_+\rightarrow\mathbb{R}_+$ be a positive, in …
- 67
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0
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Optimization over the set of all bounded probability measures
Given $X$ finite, fix a continuous function $\theta \in \Delta^+ (X) \to [0,1]$, fix a probability measure $\mu^*$, and a $\varepsilon > 0$. Consider:
$$
\max_{\mu \in \Delta^+ (X)} \theta (\mu), \qua …
- 67