2021
DOI: 10.48550/arxiv.2110.14072
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Abstract: Backtracking is an inexact line search procedure that selects the first value in a sequence π‘₯ 0 , π‘₯ 0 𝛽, π‘₯ 0 𝛽 2 ... that satisfies 𝑔(π‘₯) ≀ 0 on R + with 𝑔(π‘₯) ≀ 0 iff π‘₯ ≀ π‘₯ * . This procedure is widely used in descent direction optimization algorithms with Armijo-type conditions. It both returns an estimate in (𝛽π‘₯ * , π‘₯ * ] and enjoys an upper-bound ⌈log 𝛽 πœ–/π‘₯ 0 βŒ‰ on the number of function evaluations to terminate, with πœ– a lower bound on π‘₯ * . The basic bracketing mechanism employed in sever… Show more

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