Two derivative-free projection approaches for systems of large-scale nonlinear monotone equations

  • Authors:

  • Masoud Ahookhosh;Keyvan Amini;Somayeh Bahrami

  • Affiliations:

  • Faculty of Mathematics, University of Vienna, Vienna, Austria 1090;Department of Mathematics, Faculty of Science, Razi University, Kermanshah, Iran;Department of Mathematics, Faculty of Science, Razi University, Kermanshah, Iran

  • Venue:
  • Numerical Algorithms
  • Year:
  • 2013

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Abstract

This study proposes two derivative-free approaches for solving systems of large-scale nonlinear equations, where the underlying functions of the systems are continuous and satisfy a monotonicity condition. First, the framework generates a specific direction then employs a backtracking line search along this direction to construct a new point. If the new point solves the problem, the process will be stopped. Under other circumstances, the projection technique constructs an appropriate hyperplane strictly separating the current iterate from the solutions of the problem. Then the projection of the new point onto the hyperplane will determine the next iterate. Thanks to the low memory requirement of derivative-free conjugate gradient approaches, this work takes advantages of two new derivative-free conjugate gradient directions. Under appropriate conditions, the global convergence result of the recommended procedures is established. Preliminary numerical results indicate that the proposed approaches are interesting and remarkably promising.