11 problems

Conditioning conjecture. The global optima of the underlying optimization problem are among the best-conditioned eigenvalues of the rectangular multiparameter eigenvalue problem.

Spurious-minima growth conjecture. Based on numerical experiments, the number of spurious local minima in $S^2$ increases “dramatically” with the number of points.

Superiorization robustness explanation conjecture. The observed robustness of the superiorization methodology with respect to increasing condition numbers is due to the fact that i…

For each dimension $n=10,\ldots,16$, the authors numerically optimized lattices and, in five cases, identified the optimized lattice with an exact lattice. Optimality conjecture. T…

Let $H \in \operatorname{Herm}(n)$ and $S_0,\ldots,S_m \in \operatorname{Sym}(n)$, and let $m_{h S_0 \ldots S_m}$ denote the quantity optimized in the paper. An upper bound for thi…

Consider the discretized problem with discretization parameter $N$, its smallest eigenvalue, and its optimal value, together with the corresponding original problem. Monotonicity a…

For a bilevel optimization problem among the 38 problems for which the Gauss–Newton method could not be implemented because the direction matrix was singular for one or more values…

The limited-memory BFGS method with displacement aggregation, denoted texttt{Agg-BFGS}, is applied repeatedly to curvature information over a sequence of iterations. The resulting…

Let $W_h$ denote the step produced by the Newton-like method, and let $\lVert W_h\rVert_{E_h}$ be its norm in the discrete deformation space. Suppose the geometry condition is the…

In numerical experiments with tensor and accelerated tensor methods, let $M_p$ denote the Lipschitz constant of the $p$-th derivative used in the complexity bounds. The experiments…

Local-minimum conjecture. When this occurs, the optimization is most likely stuck near a local minimum of $F_{\varepsilon}$.