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regularisation

Trust-region and other regularisations of linear least-squares problems

Published: 2008/02/03, Updated: 2011/04/14
  • Coralia Cartis
  • Nicholas I. M. Gould
  • Philippe L. Toint
  • Categories Nonlinear Systems and Least-Squares Tags linear least-squares, regularisation, secular equation, trust-region methods

    We consider methods for regularising the least-squares solution of the linear system Ax = b. In particular, we propose iterative methods for solving large problems in which a trust-region bound ||x||

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    alternating direction method of multipliers approximation algorithms augmented lagrangian method bilevel optimization Branch-and-Bound branch-and-cut chance constraints column generation combinatorial optimization complexity compressed sensing conic optimization convex optimization cutting planes decomposition derivative-free optimization distributionally robust optimization duality dynamic programming first-order methods global convergence global optimization heuristics integer programming interior point methods large-scale optimization linear programming machine learning mixed-integer linear programming mixed-integer nonlinear programming mixed-integer programming nonconvex optimization nonlinear optimization nonlinear programming nonsmooth optimization optimal control optimization proximal point algorithm quadratic programming robust optimization semidefinite programming stochastic optimization stochastic programming trust-region methods unconstrained optimization

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