05865915

j

05865915 Attouch, H. Soubeyran, A. Local search proximal algorithms as decision dynamics with costs to move. Set-Valued Var. Anal. 19, No. 1, 157-177 (2011). 2011 Springer, Dordrecht EN costs-to-move decision dynamics exploration process friction inertia local optimization local search algorithms proximal algorithms worthwhile-to-move incremental process

doi:10.1007/s11228-010-0139-7

Summary: Acceptable moves for the ``worthwhile-to-move'' incremental principle are such that ``advantages-to-move'' are higher than some fraction of ``costs-to-move''. When combined with optimization, this principle gives raise to adaptive local search proximal algorithms. Convergence results are given in two distinctive cases, namely low local costs-to-move and high local costs-to-move. In this last case, one obtains a dynamic cognitive approach to Ekeland's $\varepsilon$-variational principle. Introduction of costs-to-move in the algorithms yields robustness and stability properties.