{"action":"created","issue":{"url":"https://api.github.com/repos/anriseth/LineSearches.jl/issues/7","repository_url":"https://api.github.com/repos/anriseth/LineSearches.jl","labels_url":"https://api.github.com/repos/anriseth/LineSearches.jl/issues/7/labels{/name}","comments_url":"https://api.github.com/repos/anriseth/LineSearches.jl/issues/7/comments","events_url":"https://api.github.com/repos/anriseth/LineSearches.jl/issues/7/events","html_url":"https://github.com/anriseth/LineSearches.jl/pull/7","id":181895737,"number":7,"title":"Backtracking line search with interpolation","user":{"login":"cortner","id":7688515,"avatar_url":"https://avatars.githubusercontent.com/u/7688515?v=3","gravatar_id":"","url":"https://api.github.com/users/cortner","html_url":"https://github.com/cortner","followers_url":"https://api.github.com/users/cortner/followers","following_url":"https://api.github.com/users/cortner/following{/other_user}","gists_url":"https://api.github.com/users/cortner/gists{/gist_id}","starred_url":"https://api.github.com/users/cortner/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/cortner/subscriptions","organizations_url":"https://api.github.com/users/cortner/orgs","repos_url":"https://api.github.com/users/cortner/repos","events_url":"https://api.github.com/users/cortner/events{/privacy}","received_events_url":"https://api.github.com/users/cortner/received_events","type":"User","site_admin":false},"labels":[],"state":"open","locked":false,"assignee":null,"assignees":[],"milestone":null,"comments":5,"created_at":"2016-10-09T16:20:23Z","updated_at":"2016-10-09T22:49:01Z","closed_at":null,"pull_request":{"url":"https://api.github.com/repos/anriseth/LineSearches.jl/pulls/7","html_url":"https://github.com/anriseth/LineSearches.jl/pull/7","diff_url":"https://github.com/anriseth/LineSearches.jl/pull/7.diff","patch_url":"https://github.com/anriseth/LineSearches.jl/pull/7.patch"},"body":"This PR adds a second backtracking line search, `interpbacktrack_linesearch!` which, instead of an a *= rho update performs an interpolation step; this is highly efficient for some problems; see QCG and QLBFGS in the following figure (from my own research); \r\n<img width=\"543\" alt=\"optim\" src=\"https://cloud.githubusercontent.com/assets/7688515/19221917/5d9fa264-8e44-11e6-854c-46c4c973e745.png\">\r\n\r\nIt also outperforms HZ and MT line-search for some more standard model problems.  In general, it is no worse than standard backtracking, which I left only for the sake of compatibility. I would actually recommend to remove standard backtracking altogether and replace it with `interpbacktrack`.\r\n"},"comment":{"url":"https://api.github.com/repos/anriseth/LineSearches.jl/issues/comments/252518676","html_url":"https://github.com/anriseth/LineSearches.jl/pull/7#issuecomment-252518676","issue_url":"https://api.github.com/repos/anriseth/LineSearches.jl/issues/7","id":252518676,"user":{"login":"anriseth","id":5601805,"avatar_url":"https://avatars.githubusercontent.com/u/5601805?v=3","gravatar_id":"","url":"https://api.github.com/users/anriseth","html_url":"https://github.com/anriseth","followers_url":"https://api.github.com/users/anriseth/followers","following_url":"https://api.github.com/users/anriseth/following{/other_user}","gists_url":"https://api.github.com/users/anriseth/gists{/gist_id}","starred_url":"https://api.github.com/users/anriseth/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/anriseth/subscriptions","organizations_url":"https://api.github.com/users/anriseth/orgs","repos_url":"https://api.github.com/users/anriseth/repos","events_url":"https://api.github.com/users/anriseth/events{/privacy}","received_events_url":"https://api.github.com/users/anriseth/received_events","type":"User","site_admin":false},"created_at":"2016-10-09T22:49:01Z","updated_at":"2016-10-09T22:49:01Z","body":"I had a look in Nocedal and Wright - Numerical Optimization. \r\nThis algorithm is described as an enhancement to standard backtracking, found in Chapter 3, the section on Interpolation (page 56 in my edition).\r\n\r\nThey go one step further: \r\nIn the first iteration they use quadratic interpolation, and then a cubic interpolation with the two previous alpha-values, i.e. f(0), f'(0), f(α_{k}), f(α_{k-1}) \r\n"}}
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