Accession Number : AD0727487

Title :   A Duality Theorem for Convolution,

Corporate Author : ISTITUTO PER LE APPLICAZIONI DEL CALCOLO ROME (ITALY)

Personal Author(s) : Altman,Mieczyslaw

Report Date : 14 FEB 1970

Pagination or Media Count : 12

Abstract : The theory of conjugate functions gives an elegant and powerful tool to investigate certain aspects of optimization theory. It is especially useful for the development of the duality theory for such problems. In this connection this paper discusses a general duality theorem for the convolution. Two aspects of this theorem should be emphasized. The first aspect shows the algebraic character of the problem. More precisely, no topology is imposed on the linear space for which this theorem can be formulated and proved. The second aspect of this theorem shows that the well-known duality theorem for the minimum distance problem is a special case of the above mentioned theorem. Moreover, as another consequence of the duality theorem for convolution the author obtains a generalization of the duality theorem for the minimum distance problem by replacing the 'distance' by an arbitrary real valued convex function. (Author)

Descriptors :   (*MATHEMATICAL PROGRAMMING, FUNCTIONS), CONVEX SETS, OPTIMIZATION, THEOREMS, ITALY

Subject Categories : Theoretical Mathematics
      Operations Research

Distribution Statement : APPROVED FOR PUBLIC RELEASE