11 problems

The experiments concern the semi-smooth Newton method applied to positively constrained convex quadratic programming problems whose matrix $Q\in\mathbb R^{n\times n}$ does not sati…

Let $f,g_1,\ldots,g_m$ be the functions defining the set ${\rm U}(f,g_1,\ldots,g_m)$ in the surrounding quadratic-system framework. Lara–Urruty's conjecture. The convexity of the s…

Consider a minimax quadratic optimization problem with outer variable $x\in\mathbb{R}^{n_x}$, inner variable $y\in\mathbb{R}^{n_y}$, objective … subject to coupled constraints…

Variational-representation extension conjecture. Similar representations should be derivable for arbitrary cost matrices, still under the finitely discrete setting, using similar t…

Lipschitz continuity conjecture for the convex QCQP reformulation. If the paper's assumptions $Cref{assum:Ab}$ and $ref{assum:main}$ hold and $k>0$, then for every…

Let $S$ be defined by an arbitrary number of ball constraints, and let ${\cal D}:=\operatorname{cone}\{(xx^\top,x):~x\in S\}\subseteq {\mathbb{S}}^n_+\oplus {\mathbb{R}}^n$ be the…

Let $\text{\sc Beta}$ denote the convex relaxation of the ball-constrained nonconvex quadratic program defined in the paper, with matrix variable $W$ and vectors $\ell_1,\ell_2$ as…

Let $n$ be a positive integer, let $P_x$ be the region associated with a sign vector $x\in\{-1,+1\}^n$, and let $(C,c)$ be a quadratic-programming input. The preceding proposition…

Let $n$ be the dimension parameter, and let $(C,c)$ be the randomly sampled input used by algorithm. The algorithm repeatedly applies Step. The iteration-bound conjecture. terminat…

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…

The alternating direction method of multipliers (ADMM) is applied to quadratic optimization problems, and its iterates are considered near an optimal solution. Boley's local linear…