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Primal-Dual Formulations for Parameter Estimation Problems

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(1)Primal-Dual Formulations for Parameter Estimation Problems Guy Chavent, Karl Kunisch, Jean Roberts. To cite this version: Guy Chavent, Karl Kunisch, Jean Roberts. Primal-Dual Formulations for Parameter Estimation Problems. [Research Report] RR-2891, INRIA. 1996. �inria-00073799�. HAL Id: inria-00073799 https://hal.inria.fr/inria-00073799 Submitted on 24 May 2006. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés..

(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. Primal-Dual Formulations for Parameter Estimation Problems Guy Chavent,. Karl Kunisch. and. Jean E. Roberts. N˚ 2891 May 1996. THÈME 4. ISSN 0249-6399. apport de recherche.

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(238) # M  O M  g   K lq \ K \ O cdfXAP y+H O  M PRUT      T6½.   O  M#  .   .  . .   b \ K \ O dfXYP b    H.  › Z gb x Z bgq K 3 £ ‰s‰VP £ YTZ bcq ]wk t qmh Z ]un | j:j œ j œ {| j>nBjsqobžhibcj>k 3 £ 3 £ = ])xwj>kƒxzegd t ])h Z bgqnŽf | fs | fXn Z ›³bžh Z h Z ]’fXkŽfXežvNq€bgq j œ h Z ]Rxwjsk±s]zy:bžh¢v n | j>nB] | hobg] q j œ h Z ]uxwjsqoh œ dƒkƒxzhibcj>kŽfXe  |KMNH.O HL# PSR   K+M<H:O P ‰  KMNH.O H#LP  g bgWk K' P £ = ]usbž>] µ | q€h h Z ]uqi] xwj>k t.t ] | bžsfDhibž>]¤j œ  £ • » » “ ý”  »   [   KMNH.O HL# P  &    g   '# R       K H,+ H P  &      R T  $  

(239)  # H +^P   K+M<H:OH # PvK QH +<H P R

(240)  ‰ d # M + † K oO g M"b M   bhg   M K 3 £ ‰Aˆ P g • »\»  ˜  bž¦ ] | ]wk™hob¥fXhobgk6h¢›³bcxw]ubgWk K 3 £ 3 Pr½6h Z ] t ] µ k6bžhibcj>k j œ  ½ƒ›W]¤j>Ÿ6hrfXbck g

(241)  

(242). 

(243). # K$A# H P  K+MNH.O H# PvK QH <+ H P R b b g † K oO H + ^ P d † g M g  M g g

(244)

(245) ‰ M b + bg    M b bhg  ] µ kƒ]  R d M #  M +  .  . . .  Þ  ú. .

(246) 

(247)      !" # %$&'$&)(*& +,-. /0 1$&2. †. fsk t qidƒŸ6qohibžhrdNhr] œ j | bckh Z ] h Z b | t hi] | ^ j œ h Z ] | bc Z ho© Z fsk t qob t ]

(248)  KMNH.O HL# PK QH +<H P R

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