Memory is a key computational bottleneck when solving large-scale convex optimization problems, such as semidefinite programs (SDPs). In this paper, we focus on the regime in which storing an $n\times n$ matrix decision variable prohibitive. To solve SDPs regime, develop randomized algorithm that returns random vector whose covariance near-feasible and near-optimal for SDP. We show how to by mo...

For f ∈ H2, let Gf := {g ∈ zH : f + g ∈ L∞ and Tf+g is hyponormal}. In 1988, C. Cowen posed the following question: If g ∈ Gf is such that λ g / ∈ Gf (all λ ∈ C, |λ| > 1), is g an extreme point of Gf ? In this note we answer this question in the negative. At the same time, we obtain a general sufficient condition for the answer to be affirmative; that is, when f ∈ H∞ is such that rankHf < ∞.

We study the extreme and periodic&nbsp;$L_2$ discrepancy of plane point sets. The is based on arbitrary rectangles as test sets whereas periodic uses “periodic intervals”, which can be seen intervals t