TITLE:
On Continuous Programming with Support Functions
AUTHORS:
Iqbal Husain, Santosh K. Shrivastav, Abdul Raoof Shah
KEYWORDS:
Continuous Programming; Second-Order Generalized Invexity; Second-Order Duality; Nonlinear Programming; Support Functions; Natural Boundary Values
JOURNAL NAME:
Applied Mathematics,
Vol.4 No.10,
October
14,
2013
ABSTRACT:
A second-order Mond-Weir type dual problem is formulated
for a class of continuous programming problems in which both objective and
constraint functions contain support functions; hence it is nondifferentiable.
Under second-order strict pseudoinvexity, second-order pseudoinvexity and
second-order quasi-invexity assumptions on functionals, weak, strong, strict
converse and converse duality theorems are established for this pair of dual
continuous programming problems. Special cases are deduced and a pair of dual
continuous problems with natural boundary values is constructed. A close
relationship between the duality results of our problems and those of the
corresponding (static) nonlinear programming problem with support functions is
briefly outlined.