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A modified BFGS method and its global convergence in nonconvex minimization. (English) Zbl 0984.65055
A modification of the BFGS method for unconstrained optimization is proposed. The authors study the following unconstrained optimization problem: $\min f(x)$, $x\in\bbfR^n$, where $f: \bbfR^n\to \bbfR$ is continuously differentiable function. The objective function $f$ has Lischitz continuous gradients. Main result: The authors show (the precise proofs are given) a global convergence property even without convexity assumption on the objective function. Under certain conditions superlinear convergence of the proposed method is presented.

MSC:
65K05Mathematical programming (numerical methods)
90C26Nonconvex programming, global optimization
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References:
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