A FARKAS LEMMA FOR DIFFERENCE SUBLINEAR SYSTEMS AND QUASIDIFFERENTIABLE PROGRAMMING

A new generalized Farkas theorem of die alternative is presented for s ystems involving functions which can be expressed as the difference of sublinear functions. Various other forms of theorems of the alternati ve are also given using quasidifferential calculus. Comprehensive opti mality conditions are then developed for broad classes of infinite dim ensional quasidifferentiable programming problems. Applications to dif ference convex programming and infinitely constrained concave minimiza tion problems are also discussed.