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Article Dans Une Revue Computational Optimization and Applications Année : 2022

OFFO minimization algorithms for second-order optimality and their complexity

Résumé

An Adagrad-inspired class of algorithms for smooth unconstrained optimization is presented in which the objective function is never evaluated and yet the gradient norms decrease at least as fast as O(1/k+1−−−−√) while second-order optimality measures converge to zero at least as fast as O(1/(k+1)1/3). This latter rate of convergence is shown to be essentially sharp and is identical to that known for more standard algorithms (like trust-region or adaptive-regularization methods) using both function and derivatives’ evaluations. A related “divergent stepsize” method is also described, whose essentially sharp rate of convergence is slighly inferior. It is finally discussed how to obtain weaker second-order optimality guarantees at a (much) reduced computational cost.

Dates et versions

hal-03993071 , version 1 (16-02-2023)

Identifiants

Citer

Serge Gratton, Philippe L. Toint. OFFO minimization algorithms for second-order optimality and their complexity. Computational Optimization and Applications, 2022, 84, pp.573-607. ⟨10.1007/s10589-022-00435-2⟩. ⟨hal-03993071⟩
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