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problem function algorithm solution programming result model theorem point lemma method proof optimization matrix value vector section program number duality condition order distribution semide nite programming objective system approach research class jt +1 approximation direction ellipsoid 0.0 constraint demand ellipsoid algorithm paper sequence iteration parameter allocation semide university operation optimization problem location customer yield inequality relation example matrice zhang table revenue analysis process max function application d-induced space report 1 t t probability information version theory mapping subject management operations research simulation product equation fare classes decision objective function notice 2.1