Accession Number : AD0665318

Title :   DUALITY IN DISCRETE PROGRAMMING: II. THE QUADRATIC CASE.

Descriptive Note : Research rept.,

Corporate Author : CARNEGIE-MELLON UNIV PITTSBURGH PA MANAGEMENT SCIENCES RESEARCH GROUP

Personal Author(s) : Balas,Egon

Report Date : DEC 1967

Pagination or Media Count : 14

Abstract : The paper extends the results of 'Duality in Discrete Programming' (1) to the case of quadratic objective functions. The paper is, however, self-contained. A pair of symmetric dual quadratic programs is generalized by constraining some of the variables to belong to arbitrary sets of real numbers. Quadratic all-integer and mixed-integer programs are special cases of these problems. The resulting primal problem is shown, subject to a qualification, to have an optimal solution if and only if the dual has one, and in this case the values of their respective objective functions are equal. Most of the other results of (1) are also shown to carry over to the quadratic case. (Author)

Descriptors :   (*QUADRATIC PROGRAMMING, *OPERATIONS RESEARCH), MINIMAX TECHNIQUE, REAL NUMBERS, MATHEMATICAL PROGRAMMING, THEOREMS, INEQUALITIES

Subject Categories : Operations Research

Distribution Statement : APPROVED FOR PUBLIC RELEASE