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: \(\min f(x)\), \(x\in\mathbb{R}^n\), where \(f: \mathbb{R}^n\to \mathbb{R}\) 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.


65K05 Numerical mathematical programming methods
90C26 Nonconvex programming, global optimization


Full Text: DOI


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