16 problems

Consider the aggregation schemes for the Hamiltonian-flow trajectory used to choose the next iterate in convex optimization, including the uniform average and the minimizer along t…

The adaptive delayed-update cyclic algorithm is defined with step sizes and extrapolation weights as above, where $bc$ denotes the strong convexity parameter used in the theoretica…

An algorithm of Lur'e form is an algorithm described by the Lur'e system and gradient-input relation referred to in the source. Lessard's proximal-variant conjecture. Any algorithm…

Asymptotic-rate conjecture. The exact sublinear rates for regimes $p_5$ and $p_6$ correspond to

Finite-iteration tightness conjecture. The DCA rates corresponding to regimes $p_1$, $p_2$, $p_3$ and $p_4$ are tight for any number of iterations $N$.

Consider the subgradient method for minimizing a function with initial-distance parameter $R$ and subgradient-bound parameter $B$, and suppose that its step sizes are chosen indepe…

The setting concerns geodesically strongly-convex-strongly-concave min-max optimization on geodesic metric spaces and its Euclidean counterpart, where existing methods exhibit an e…

Discretization hypothesis. The reduced oscillations of the IGAHD method are a consequence of the more subtle discretization underlying it.

The paper compares accelerated gradient descent (AGD) with gradient descent for nonconvex optimization and identifies the momentum parameter as crucial to its nonconvex complexity…

Let $\mathcal{K}$ be the feasible set, let $alpha_t$ denote the weights used by the framework, and let $A_T=sum_{t=1}^T alpha_t$. The analysis above identifies the choice…

In the three-dimensional compliance problem, let $D\theta$ denote the derivative used by the $\mathbb{R}^n$ algorithm and let $\nabla\theta=\mathbf{M}^{-1}D\theta$ denote the gradi…

The Bregman Proximal DC Algorithm (BPDCA) and its extrapolated variant BPDCAe are algorithms for DC optimization problems, using a kernel generating distance $h$ and an $L$-smooth…

Consider the quadratic min-max game … Here $\mathbb{H}=\mathbb{G}:=\mathbb{R}_{\theta=90^\circ}\Lambda\mathbb{R}_{\theta=90^\circ}^T$,…

IQC improvement conjecture. By using off-by-one IQCs or other IQCs developed in the cited work within this Lyapunov framework, one can further improve the numerical bounds.

Primal-dual explanation conjecture. This phenomenon is due to the primal-dual nature of the DC algorithm, in contrast to the first-order primal descent of GIST.

Let $G$ be an algorithm of the form referred to as, and suppose that it converges with rate $\rho$. A proximal variant is obtained by replacing the relevant operator with its proxi…