The extended Smale's 9th problem -- On computational barriers and paradoxes in estimation, regularisation, computer-assisted proofs and learning

Understand

Linear and semidefinite programming (LP, SDP), regularisation through basis pursuit (BP) and Lasso have seen great success in mathematics, statistics, data science, computer-assisted proofs and learning.

• The success of LP is traditionally attributed to the fact that it is "in P" for rational inputs.
• On the other hand, in his list of problems for the 21st century S.
• Smale calls for "[Computational] models which process approximate inputs and which permit round-off computations".