Tagged Questions

Convex analysis is the study of properties of convex sets and convex functions. For questions about optimization of convex functions over convex sets, please use the (convex-optimization) tag.

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Why is this matrix symmetric?

There is an example in the Convex Optimization lecture notes, Boyd. He just said in the lecture that the matrix which is underlined in red color is symmetric! How can we claim that when there is no ...
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how to calculate infimum of Augmented Lagrangian?

should any body explain that how do we calculate these step? \begin{align*} L(x,y) &= f(x) + y^T(Ax-b)\\ g(y) &= \inf_x \, L(x,y) \\ &= \inf_x \, f(x) - \langle -A^Ty, x \rangle - \langle ...
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Is the smallest ellipsoid enclosing a convex set unique?

Let $S \subset \mathbb{R}^n$ be a convex set. Assume that it is bounded. We want to find an ellipsoid $E$ of smallest volume such that $S \subset E$. Is $E$ unique?
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Is $\frac{F}{A}+c_p D K \sqrt{A}+c_g \Theta^2+c_e a D + t e (1-\Theta) D+ \frac{t a}{A}$ quasiconvex?

I am trying to check if the following function is jointly quasiconvex in $A>0,a,\theta \geq 0$. $$\frac{F}{A}+c_p D K \sqrt{A}+c_g \Theta^2+c_e a D + t e (1-\Theta) D+ \frac{t a}{A}$$ The ...
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Width of a cone

Let $V=\{v_k\}$ be a collection of vectors of $\Bbb{R}^n$, and define their cone to be the set of all their non-negative linear combinations: $$C(V):=\Big\{ \sum_k a_k\,v_k; \; a_k\ge 0 \Big\}\;.$$ ...
Question: Consider a fixed number $k > 3$ of random points in the plane, each independently distributed according to a 2D standard normal distribution. What is the probability that the convex hull ...