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Nonmonotone spectral gradient-type methods for large-scale unconstrained optimization and nonlinear systems of equations. (English) Zbl 1228.49038
Summary: This paper presents some spectral gradient-type methods under a new non-monotone line search, which possesses a favorite property that each iteration is well defined even when the search direction is not a descent direction. That may be useful when the function values are inaccurate (e.g., in real-life problems, the values are sometimes noised or derivatives are computed by differences). Global convergence is established under some suitable conditions and a nonmonotone Spectral Conjugate Gradient (SCG) method is presented as a special case. Then this SCG method is extended to solve nonlinear systems of equations, which results in a new derivative-free method for solving large-scale nonlinear equations. Preliminary numerical results are reported on a set of large-scale problems to show the convergence and efficiency of this method.
49M37Methods of nonlinear programming type in calculus of variations
65H10Systems of nonlinear equations (numerical methods)
65K05Mathematical programming (numerical methods)
90C26Nonconvex programming, global optimization
90C30Nonlinear programming
93A15Large scale systems