Hybrid Gauss-Newton Method for Convex Inclusion and Convex-Composite Optimization Problems

In Banach space optimization, solving inclusion and convex-composite problems through iterative methods depends on various convergence conditions. In this work, we develop an extended semi-local convergence analysis for two algorithms used to generate sequences converging to solutions of inclusion and convex-composite optimization problems for Banach space-valued operators. The applicability of these algorithms is extended with benefits: weaker sufficient convergence criteria and tighter error estimates on the distances involved. These advantages are obtained at the same computational cost since the Lipschitz constants used are special cases of the Lipschitz constant used in earlier studies. The implementation issues for these algorithms are also addressed by introducing hybrid algorithms.