{"http:\/\/dx.doi.org\/10.14288\/1.0364458":{"http:\/\/vivoweb.org\/ontology\/core#departmentOrSchool":[{"value":"Non UBC","type":"literal","lang":"en"}],"http:\/\/www.europeana.eu\/schemas\/edm\/dataProvider":[{"value":"DSpace","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/creator":[{"value":"Bot, Radu Ioan","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/issued":[{"value":"2018-03-25T05:02:14Z","type":"literal","lang":"*"},{"value":"2017-09-19T17:37","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/description":[{"value":"The possibilities of exploiting the special structure of d.c. programs, which\nconsist of optimizing the difference of convex functions, are currently more\nor less limited to variants of the DCA proposed by Pham Dinh Tao and Le\nThi Hoai An in 1997. These assume that either the convex or the concave\npart, or both, are evaluated by one of their subgradients.
\n\nIn this talk we propose an algorithm which allows the evaluation of both\nthe concave and the convex part by their proximal points. Additionally, we\nallow a smooth part, which is evaluated via its gradient. In the spirit of\nprimal-dual splitting algorithms, the concave part might be the composition\nof a concave function with a linear operator, which are, however, evaluated\nseparately.
\n\nFor this algorithm we show that every cluster point is a solution of the\noptimization problem. Furthermore, we show the connection to the Toland\ndual problem and prove a descent property for the objective function values\nof a primal-dual formulation of the problem. Convergence of the iterates is\nshown if this objective function satisfies the Kurdyka - Lojasiewicz property.\nIn the last part, we apply the algorithm to an image processing model.
\n\nThe talk relies on a joint work with Sebastian Banert.","type":"literal","lang":"en"}],"http:\/\/www.europeana.eu\/schemas\/edm\/aggregatedCHO":[{"value":"https:\/\/circle.library.ubc.ca\/rest\/handle\/2429\/64928?expand=metadata","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/extent":[{"value":"39 minutes","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/elements\/1.1\/format":[{"value":"video\/mp4","type":"literal","lang":"en"}],"http:\/\/www.w3.org\/2009\/08\/skos-reference\/skos.html#note":[{"value":"","type":"literal","lang":"en"},{"value":"Author affiliation: University of Vienna","type":"literal","lang":"en"}],"http:\/\/www.europeana.eu\/schemas\/edm\/isShownAt":[{"value":"10.14288\/1.0364458","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/language":[{"value":"eng","type":"literal","lang":"en"}],"https:\/\/open.library.ubc.ca\/terms#peerReviewStatus":[{"value":"Unreviewed","type":"literal","lang":"en"}],"http:\/\/www.europeana.eu\/schemas\/edm\/provider":[{"value":"Vancouver : University of British Columbia Library","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/publisher":[{"value":"Banff International Research Station for Mathematical Innovation and Discovery","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/rights":[{"value":"Attribution-NonCommercial-NoDerivatives 4.0 International","type":"literal","lang":"en"}],"https:\/\/open.library.ubc.ca\/terms#rightsURI":[{"value":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/","type":"literal","lang":"en"}],"https:\/\/open.library.ubc.ca\/terms#scholarLevel":[{"value":"Faculty","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/isPartOf":[{"value":"BIRS Workshop Lecture Videos (Oaxaca de Ju\u00e1rez (Mexico))","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/subject":[{"value":"Mathematics","type":"literal","lang":"en"},{"value":"Operations research, mathematical programming","type":"literal","lang":"en"},{"value":"Operator theory","type":"literal","lang":"en"},{"value":"Control\/optimization\/operation research","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/title":[{"value":"A general double-proximal gradient algorithm for d.c. programming","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/type":[{"value":"Moving Image","type":"literal","lang":"en"}],"https:\/\/open.library.ubc.ca\/terms#identifierURI":[{"value":"http:\/\/hdl.handle.net\/2429\/64928","type":"literal","lang":"en"}]}}