Algorithm for the generalized Φ-strongly monotone mappings and application to the generalized convex optimization problem.
Aibinu, M. O.
Mewomo, O. T.
Let E be a uniformly smooth and uniformly convex real Banach space and E∗ be its dual space. We consider a multivalued mapping A : E → 2E∗ which is bounded, generalized Φ-strongly monotone and such that for all t > 0, the range R(Jp+tA) = E∗, where Jp (p > 1) is the generalized duality mapping from E into 2E∗ . Suppose A−1(0) = ∅, we construct an algorithm which converges strongly to the solution of 0 ∈ Ax. The result is then applied to the generalized convex optimization problem.