APPROXIMATE SUBDIFFERENTIALS AND NONSMOOTH ANALYSIS FINITE DIMENSIONS  

作　　者：WANG Yuntong (Nankai Institute of Mathematics,Tianjin 300071,China) 

出　　处：《Systems Science and Mathematical Sciences》1992年第1期84-96,共13页

摘　　要：Ioffe’s approximate subdifferentials are reviewed and some of his resultsare generalized.An extension of the calculus of the approximate subdifferentials forthe sums to any finite number of functions is provided along with a generalizationof the Dubovitzkii-Milyutin theorem.The presentation also indicates some of thelimitations of nonsmooth analysis and optimization.Restriction to the class offunction which is suitable for most of the purposes in nonsmooth optimization issuggested.Ioffe's approximate subdifferentials are reviewed and some of his resultsare generalized.An extension of the calculus of the approximate subdifferentials forthe sums to any finite number of functions is provided along with a generalizationof the Dubovitzkii-Milyutin theorem.The presentation also indicates some of thelimitations of nonsmooth analysis and optimization.Restriction to the class offunction which is suitable for most of the purposes in nonsmooth optimization issuggested.

关 键 词：APPROXIMATE SUBDIFFERENTIALS Dini SUBDIFFERENTIAL Clarke generalized gradient CONTINGENT CONE Clarke TANGENT CONE normal CONE regular function strong general position property SUBDIFFERENTIAL calculus 

分 类 号：N94[自然科学总论—系统科学]