Questions tagged [convex-optimization]

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5
votes
0answers
67 views

Convexity of the projection of a convex set

Question: A set $S \subset \mathbb{R}^m \times \mathbb{R}^n$ is convex. Using the fact that affine maps preserves convexity prove that $S(y) = \{x \in \mathbb{R}^m\mid (x,y)\in S \}$ and $\hat{S} = ...
8
votes
2answers
113 views

Convex Optimization: Separation of Cones

I am trying to solve Exercise 2.39 at Boyd and Vandenberghe's Convex Optimization book. In one source, the answer is given as: 2.39 Separation of cones. Let $K$ and $\tilde K$ be two convex cones ...
8
votes
4answers
205 views

Disciplined convex programming representation of $x\sqrt{1-x}$

Anyone have an idea for a disciplined convex programming (DCP) representation of the concave function $x\sqrt{1-x}$, which is defined over the domain $[0,1]$? The Taylor series about $x=0$ is $$x - \...
8
votes
1answer
215 views

Convexity/Concavity of Average Number of Jobs in M/M/1 Queue?

I am working on a problem involving the average number of jobs $L$ in an M/M/1 queue with arrival rate $\lambda$, service rate $\mu$. For traffic intensity $\rho = \frac{\lambda}{\mu}$, $$ L = \frac{\...
12
votes
2answers
168 views

Convex Maximization with Linear Constraints

I am doing active research in convex maximization w.r.t. linear constraints. There are many cases which can be efficiently approximately solved, e.g., convex quadratic maximization, log-sum-exp ...