5 problems

Let $u(n,d,R,\rho,M,\mathcal{G})$ denote the worst-case information complexity of a query strategy under the full-information first-order oracle based on a first-order chart…

Let $n$ be the number of integer variables, let $d$ be the continuous dimension, and let $M$, $R$, $\rho$, and $\varepsilon$ be the problem parameters. A first-order chart…

Let $\ell$ be a lower bound on the information complexity, with respect to a fixed oracle, for a family of continuous, constrained convex optimization instances. Mixed-integer tran…

Let $f$ be a function and let $mu$ be an input distribution. Write $f^q$ for the coordinatewise product of $f$ on $q$ independent instances, $CC_{mu^q}[f^q,0]$ for the zero-error c…

Let $\widetilde{F}_d$ be the class of smooth functions on $[0,1]^d$ defined by … Consider the question whether integration on this class suffers from the curse of dimensionality, a…