10 problems

Optimized full cyclic coordinate descent has a superlinear numerical rate
arXiv@arxiv
Let $N$ denote the iteration count, and consider full fixed-step cyclic coordinate descent on a problem partitioned into $2$ blocks, allowing the update to use all past gradient in…
Conjectureopencoordinate-descent first-order-methods optimization
0
RPCD worst-case conjecture for positive-definite quadratics
arXiv@arxiv
RPCD worst-case conjecture. The upper bound above, proved for the specified permutation-invariant class of quadratic Hessians, extends to all positive-definite quadratic functions.…
Conjectureopencoordinate-descent optimization random-permutations
1
Conjecture on the sparsity advantage of Mixing Method++
arXiv@arxiv
Let $C$ be a matrix, and compare Mixing Method++ with Mixing Method on problems having different sparsity levels, where sparsity is the number of zero-valued elements divided by th…
Conjectureopencoordinate-descent optimization semidefinite-programming
0
The RPCD versus RCD expected-performance conjecture
arXiv@arxiv
Let RPCD denote randomized-permutation coordinate descent and RCD denote randomized coordinate descent, and interpret their performance through the expected objective values after…
Conjectureopencoordinate-descent optimization randomized-algorithms
0
Convergence conjecture for the coordinate-descent PARAFAC algorithm
arXiv@arxiv
Let $\{\mathbf{A}^k\}$ be the sequence generated by Algorithm, where $\mathbf{A}^k$ is the solution $(\mathbf{A}^{(1)},\mathbf{A}^{(2)},\ldots,\mathbf{A}^{(N)})$ in the $k$ -th iter…
Conjectureopencoordinate-descent optimization tensor-decomposition
1
Weight-renormalization conjecture for parallel Dykstra coordinate descent
arXiv@arxiv
Let parallel-Dykstra-CD be the parallel algorithm for the lasso problem, with convergence bound … Here the weights are the coefficients used by the parallel algorithm, and zero coe…
Conjectureopenconvergence-rates coordinate-descent optimization
1
The impossibility conjecture for an $\mathcal{O}(\frac{L}{r})$ cyclic BCGD bound
arXiv@arxiv
Let cyclic BCGD denote cyclic block coordinate gradient descent for general convex problems, and let $L$ and $r$ be the parameters used in its iteration-complexity bound. Impossibi…
Conjectureopenconvex-optimization coordinate-descent iteration-complexity
0
Conjecture on larger step sizes for the coordinate descent primal-dual algorithm
arXiv@arxiv
The algorithm uses step sizes satisfying Assumption, which generally permits larger step sizes than those suggested by the approaches of Combettes and collaborators and Bianchi and…
Conjectureopencoordinate-descent optimization primal-dual-algorithms
0
Zero-error convergence-bound conjecture for the GS- $q$ rule
arXiv@arxiv
Consider the composite objective $F(x)=f(x)+\sum_i g_i(x_i)$ and the GS- $q$ coordinate-selection rule with coordinate smoothness parameters $L_i$ . Let $\epsilon_k$ be the error ter…
Conjectureopenconvex-optimization coordinate-descent
0
Gauss–Southwell convergence-rate conjecture for general graphs
arXiv@arxiv
Let $h_2$ be the graph-structured quadratic problem considered above, and let $\rho_2^G$ denote the quantity defined for pairs of nodes. For nodes $i$ and $j$ , call them connected…
Conjectureopencoordinate-descent graph-algorithms optimization
1