Optimization landscape in the simplest constrained random least-square problem

  title={Optimization landscape in the simplest constrained random least-square problem},
  author={Yan V. Fyodorov and Rashel Tublin},
  journal={Journal of Physics A: Mathematical and Theoretical},
  • Y. Fyodorov, Rashel Tublin
  • Published 26 December 2021
  • Mathematics, Computer Science
  • Journal of Physics A: Mathematical and Theoretical
We analyze statistical features of the ‘optimization landscape’ in a random version of one of the simplest constrained optimization problems of the least-square type: finding the best approximation for the solution of a system of M linear equations in N unknowns: ( a k , x ) = b k , k = 1, …, M on the N-sphere x 2 = N. We treat both the N-component vectors a k and parameters b k as independent mean zero real Gaussian random variables. First, we derive the exact expressions for the mean number… 

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