鎶ュ憡棰樼洰錛?Best Nonnegative Rank-One Approximations of Tensors
鎶ュ憡浜猴細鑳¤儨榫欙紙鏉窞鐢靛瓙縐戞妧澶у 鏁欐巿錛?
鎶ュ憡鏃墮棿錛?019騫?鏈?0鏃?15:00
鎶ュ憡鍦扮偣錛氭牸鑷翠腑妤?00浼氳瀹?
鎶ュ憡鎽樿錛欼n this talk, we discuss the polynomial optimization problem of multi-forms over the intersection of the multi-spheres and the nonnegative orthants. This class of problems is NP-hard in general, and includes the problem of finding the best nonnegative rank-one approximation of a given tensor. A Positivstellensatz is given for this class of polynomial optimization problems, based on which a globally convergent hierarchy of doubly nonnegative (DNN) relaxations is proposed. A (zero-th order) DNN relaxation method is applied to solve these problems, resulting in linear matrix optimization problems under both the positive semidefinite and nonnegative conic constraints. A worst case approximation bound is given for this relaxation method. Then, the recent solver SDPNAL+ is adopted to solve this class of matrix optimization problems. Typically, the DNN relaxations are tight, and hence the best nonnegative rank-one approximation of a tensor can be revealed frequently.Numerical experiments is reported as well.
鎶ュ憡浜虹畝浠嬶細鑳¤儨榫欙紝鏉窞鐢靛瓙縐戞妧澶у鐞嗗闄㈡暀鎺堬紝鍗氬＋鐮旂┒鐢熷甯堛€傜爺絀舵柟鍚戜負寮犻噺浼樺寲璁＄畻鐨勭悊璁轟笌綆楁硶鍙婂叾搴旂敤銆傚厛鍚庡湪鏂板姞鍧″浗绔嬪ぇ瀛︽暟瀛︾郴鍜岃姖鍔犲摜澶у緇熻緋諱粠浜嬪崥澹悗鐮旂┒宸ヤ綔銆傚嬈″湪鍖椾含澶у鏁板瀛﹂櫌銆侀煩鍥藉浗瀹舵暟瀛︾爺絀舵墍銆佸姞宸炲ぇ瀛︿集鍏嬪埄鍒嗘牎銆侀娓悊宸ュぇ瀛︺€佹柊鍗楀▉灝斿＋澶у榪涜瀛︽湳璁塊棶銆備腑鍥借繍絳瑰浼氭暟瀛︿紭鍖栧垎浼氶潚騫寸悊浜嬶紝緹庡浗鏁板浼歁ath Review 璇勮鍛樸€?鍏辮鍙戣〃SCI 璁烘枃40 浣欑瘒錛岄儴鍒嗙爺絀舵垚鏋滃彂琛ㄥ湪鍥介檯欏剁駭鏈熷垔Numerische Mathematik銆丼IAM Journal on Matrix Analysis and Applications銆丆ommunications in Mathematical Sciences銆丣ournal of Symbolic Computation銆丣ournal of Scientific Computing銆丳hysical Review A 絳夈€?5 綃囪鏂囪鍒楀叆ESI 楂樿寮曠敤姒滐紝Web of Science 浠栧紩瓚呰繃520 嬈°€傛浘鑾稴IAM Early Career Travel Award銆丼cience China-Mathematics 浼樼璁烘枃濂栫瓑銆?
鐞嗗闄?
2019騫?鏈?鏃?
