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J Glob Optim (2007) 39:473481 DOI 10.1007/s10898-007-9150-4

Summary: J Glob Optim (2007) 39:473481
DOI 10.1007/s10898-007-9150-4
Sufficiency in multiobjective subset programming
involving generalized type-I functions
Izhar Ahmad Sarita Sharma
Received: 24 March 2006 / Accepted: 12 February 2007 / Published online: 20 April 2007
Springer Science+Business Media B.V. 2007
Abstract In this paper, sufficient optimality conditions for a multiobjective subset
programming problem are established under generalized (F, , , d)-type-I functions.
Keywords Efficient solutions Generalized n-set convex functions Sufficient
1 Introduction
The concept of optimizing n-set functions was initially developed by Morris [24],
whose results are confined only to set functions of a single set. Such type of pro-
gramming problems have various interesting applications in fluid flow [4], electrical
insulator design [7], regional design (districting, facility location, warehouse layout,
urban planning, etc.)[10,11], statistics [12,25] and optimal plasma confinement [28].
Corley [9] generalized the results of Morris [24] to n-set functions and discussed
optimality conditions and Lagrangian duality. Several authors have shown interest


Source: Ahmad, Izahr - Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals


Collections: Mathematics