Semi-Infinite Fractional Programming by Ram U. Verma

Author:Ram U. Verma
Language: eng
Format: epub, pdf
Publisher: Springer Singapore, Singapore

and hence

which in view of (i) implies

Because and is sublinear, we get

(22)

As shown in the proof of Theorem 6.8, our assumptions in (ii) and (iii) lead to (15) and (16), respectively, which when combined with (11) and (iv) yield

which contradicts (22). Therefore, we conclude that .

(b)–(e): The proofs are similar to that of part (a).

Theorem 6.21

(Strong Duality) Let be a normal efficient solution of (P) and assume that any one of the five sets of conditions set forth in Theorem 6.20 is satisfied for all feasible solutions of (DII). Then there exist indices , with , together with points indices , with , together with points for , and real numbers , with for , such that is an efficient solution of (DII) and .

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