Advances in Matrix Analysis and Optimization

The field of matrix analysis and optimization is witnessing significant developments, with a focus on improving the efficiency and scalability of algorithms. Researchers are exploring new techniques, such as compact spectral fingerprints and trust region-based methods, to tackle complex problems in matrix phylogeny, scheduling, and optimization. These innovations have the potential to advance our understanding of matrix structures and enable the development of more effective algorithms for various applications. Notably, some papers have made significant contributions to the field, including the introduction of compact spectral fingerprints for matrix phylogeny and the development of trust region-based Bayesian optimization methods for diversity optimization. For example, the paper on Matrix Phylogeny introduces a novel approach to characterizing matrices using compact spectral fingerprints, which has shown promising results in clustering and preconditioner selection. The paper on Trust Region-Based Bayesian Optimisation to Discover Diverse Solutions proposes a new method for diversity optimization using trust region-based Bayesian optimization, which has demonstrated improved performance in high-dimensional problems.

Sources

Matrix Phylogeny: Compact Spectral Fingerprints for Trap-Robust Preconditioner Selection

Scheduling Problems with Constrained Rejections

Trust Region-Based Bayesian Optimisation to Discover Diverse Solutions

None To Optima in Few Shots: Bayesian Optimization with MDP Priors

Many (most?) column subset selection criteria are NP hard

SVP$_p$ is NP-Hard for all $p > 2$, Even to Approximate Within a Factor of $2^{\log^{1-\varepsilon} n}$

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