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Results tagged with convex-optimization
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user 493556
Optimization with convex constraints and convex objectives; notions related to convex optimization such as sub-gradients, normal cones, separating hyperplanes
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Question on the closed proper convex functions
I'm confused with the definition of the closed proper convex functions when reading the paper
https://people.orie.cornell.edu/aslewis/publications/00-dykstras.pdf
It appears that, when a function $f$ …
- 1,409
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Differentiability of some function defined as the maximum
Let $d,n\ge 1$ be fixed integers. Given some compact subset $E\subset \mathbb R^d$, consider the function $f: E^n\ni (x_1,\ldots, x_n) \longrightarrow f(x_1,\ldots, x_n)\in \mathbb R$ defined by
$$f( …
- 1,409
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Boundedness of maximisers of parametric strictly concave functions
Let $L:[0,1]\times \mathbb R^m\times \mathbb R^n\to \mathbb R$ be defined by
$$L(\lambda, x,y):=\sum_{1\le i\le m}\alpha_i x_i + \sum_{1\le j\le n}\beta_j y_j -\sum_{1\le i\le m, 1\le j\le n} p_{i,j}\ …
- 1,409