Optimization and Control in Mathematical Research

The field of mathematical research is currently witnessing significant developments in optimization and control. Researchers are focusing on improving the accuracy and efficiency of various methods, including optimal recovery of unbounded operators, subspace-based methods in spectral analysis, and compressed sensing. The use of certified computational tools and novel frameworks is enabling the solution of complex problems in control theory, such as reach-avoid-stabilize and Hamilton-Jacobi reachability. Noteworthy papers in this area include:

  • A paper on an approximation framework for subspace-based methods, which introduces a mathematical framework for the approximation of eigenvalues of self-adjoint operators and provides analytical guarantees for dimension detection of spectral subspaces.
  • A paper on a dynamic working set method for compressed sensing, which proposes an efficient method for managing the working set in compressed sensing problems. These developments are expected to have a significant impact on various fields, including signal processing, control theory, and quantum physics.

Sources

On optimal recovery of unbounded operators from inaccurate data

An Approximation Framework for Subspace-based Methods in Spectral Analysis with Accuracy Guarantees

Entropy numbers of classes defined by integral operators

Reach-Avoid-Stabilize Using Admissible Control Sets

Some Computational Tools for Solving a Selection of Problems in Control Theory

A Dynamic Working Set Method for Compressed Sensing

Threshold Strategy for Leaking Corner-Free Hamilton-Jacobi Reachability with Decomposed Computations

Built with on top of