Premium
A Duality Theorem for Non‐Linear Programming
Author(s) -
Swarup K.
Publication year - 1965
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19650450506
Subject(s) - infimum and supremum , mathematics , duality (order theory) , linear programming , lagrange multiplier , duality gap , dual (grammatical number) , strong duality , fenchel's duality theorem , mathematical optimization , convex optimization , regular polygon , discrete mathematics , weak duality , optimization problem , art , geometry , literature
In this paper, a dual problem is formulated for non‐linear programming problem of minimising a convex function under concave constraints and non‐negativity restrictions on the variables (x 1 , x 2 …, x n ). The problem of P. Wolfe has been discussed with considerably reduced number of variables known as Lagrange multipliers u i . Mainly two results have been established: (a) the infimum for primal is greater or equal to the supremum of the dual under their respective constraints, (b) Principal Duality Theorem. Finally a numerical example has been solved to exhibit important results of the paper.