11 problems

Let $F$ be a macroscopic observable, and let the coefficients $a$ and $s$ define a stochastic perturbation of $F(\hat{\rho}_{Y_t})$ in the full dynamics referenced in the source. T…

Let $f^N_{(k)}$ denote the empirical measure of a genetic-algorithm particle system with population size $N$ at iteration $k$, and let $f_{(k)}$ denote the corresponding kinetic ev…

Consider the existing algorithms for efficient global optimization in the non-Bayesian setting, evaluated by worst-case simple regret. Randomization conjecture. Introducing randomn…

Let $S$ be the function class and $\mathcal{X}$ the domain, with $\mathcal{N}(S(\mathcal{X}),4\epsilon,|\cdot|_\infty)$ denoting the covering number of the restricted function clas…

Single-inequality bound conjecture. The bound in Burer's approach is equal to the best possible bound that can be obtained by adding a single linear inequality.

Sample-complexity conjecture. The associated sample complexity of such simplified algorithms is worse than that of the Piyavskii--Shubert algorithm by a non-negligible multiplicati…

Let $\mathcal E$ be a cost function on the sphere and let the initial datum be an arbitrary probability distribution, without assuming the well-preparation condition. Well-preparat…

Gao's NP-hardness conjecture. A global optimization problem is NP-hard only if its canonical dual has no solution in ${\cal S}^+_a$.

CPLEX structure-exploitation conjecture. We conjecture that this favorable outcome can be attributed to CPLEX's capability of identifying the particular structure of this formulati…

Algebraic-specification conjecture. For every admissible $\delta$, there is a quasi-admissible $\delta'$ with $\delta'>\delta$ that can be achieved by algebraically specified…

The lift-and-branch-and-bound method is a procedure for solving polynomial optimization formulations of transmission expansion planning problems with discrete investment decisions…