We demonstrate that, with a suitable rescaling, using Johnson-Lindenstrauss transforms (JLTs) in the random subspace model-based derivative-free optimization (DFO) algorithm from [Cartis&Roberts, Math. Prog. 199 (2023)] achieves an improved worst-case evaluation complexity bound compared to'unscaled'JLTs. This improved bound does not require any modification to the original algorithm or complexity analysis, and matches the best-known bound in terms of dimension dependence for model-based DFO (e.g. achieved by [Scheinberg&Chaudhry, ICM 2026] using Haar matrices in a similar framework).
A global iteration complexity bound is established for the smallest gradient norm among the first $k$ iterates for the smallest gradient norm among the first $k$ iterates when the initial sublevel set is bounded.
This work gives a deterministic and parameter-free Frank-Wolfe-type method with a global ambient-dimension-independent linear convergence rate under quadratic growth.
We propose variants of model-based trust region derivative-free algorithms that are closest to methods initially proposed and implemented by Powell. These methods rely on low degree polynomial interpolation and carefully maintain geometry of the interpolation sets. We are able to derive complexity bounds for these meth...
A. Chaudhry, K. Scheinberg, Scholar Sun· 0 citations
Four groups of subspace methods for nonlinear monotone equations, with applications to large-scale machine learning problems, using Jacobian-free subspace directions of conjugate-gradient type combined with either fixed step sizes or variable step sizes generated by the projected method of Solodov and Svaiter are intro...
M. Kimiaei, Shima Shabani, Michael Breuß· 0 citations
We study the maximization of the minimum eigenvalue under combinatorial and integrality constraints. We propose a new approach based on branch-and-bound combines entropic smoothing of the minimum eigenvalue function and Frank-Wolfe methods over concave relaxations of the constraints, thereby exploiting combinatorial st...
Deborah Hendrych, Mathieu Besançon, Sebastian Pokutta· 0 citations
We prove a dimension-free Poincar\'e inequality for isotropic unconditional log-concave probability measures, establishing the Kannan-Lov\'asz-Simonovits (KLS) conjecture in the unconditional setting. The proof combines a new application of Dunkl operator theory combined with an appropriate transformation of the log-co...
Dan Mikulincer, Ilias Zadik· 1 citation
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