Fritz John Type Duality in Nondifferentiable Continuous Programming with Equality and Inequality Constraints

Abstract

A Fritz John type dual for a nondifferentiable continuous programming problem with equality and inequality constraints which represent many realistic situations is formulated using Fritz John type optimality conditions instead of Karush-Kuhn-Tucker type conditions and thus does not require a regularity condition. Various duality results under suitable generalized convexity assumptions are derived. A pair of Fritz John type dual continuous programming with natural boundary conditions rather than fixed end points is also presented. Finally, it is pointed that our duality results can be considered as dynamic generalizations of those of a nondifferentiable nonlinear programming problem in the presence of equality and inequality constraints recently treated in the literature.