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A study on optimality and duality theorems of nonlinear generalized disjunctive fractional programming

โœ Scribed by E.E. Ammar

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
299 KB
Volume
48
Category
Article
ISSN
0895-7177

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โœฆ Synopsis

This paper is concerned with the study of necessary and sufficient optimality conditions for convex-concave generalized fractional disjunctive programming problems for which the decision set is the union of a family of convex sets. The Lagrangian function for such problems is defined and the Kuhn-Tucker Saddle and Stationary points are characterized. In addition, some important theorems related to the Kuhn-Tucker problem for saddle and stationary points are established. Moreover, a general dual problem is formulated and weak, strong and converse duality theorems are proved. Throughout the presented paper illustrative examples are given to clarify and implement the developed theory.

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## Abstract Familyโ€based association tests (FBATs) provide simple and powerful tests to detect association between a genetic marker and a diseaseโ€susceptibility locus, manifest in subjects by a phenotype or disease trait. Here we propose a new class of conditional tests for familyโ€based association