Algorithm for the generalized ?-strongly monotone mappings and application to the generalized convex optimization problem.
Keywords:Generalized Φ-strongly monotone, Surjective property, Generalized convex, Optimization
AbstractLet 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 ?-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.
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