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A \(q\)-Polak-Ribière-Polyak conjugate gradient algorithm for unconstrained optimization problems. (English) Zbl 1504.65128

Summary: A Polak-Ribière-Polyak (PRP) algorithm is one of the oldest and popular conjugate gradient algorithms for solving nonlinear unconstrained optimization problems. In this paper, we present a \(q\)-variant of the PRP \((q\)-PRP) method for which both the sufficient and conjugacy conditions are satisfied at every iteration. The proposed method is convergent globally with standard Wolfe conditions and strong Wolfe conditions. The numerical results show that the proposed method is promising for a set of given test problems with different starting points. Moreover, the method reduces to the classical PRP method as the parameter \(q\) approaches 1.

MSC:

65K10 Numerical optimization and variational techniques
05A30 \(q\)-calculus and related topics
90C26 Nonconvex programming, global optimization
90C52 Methods of reduced gradient type

Software:

CUTEr; SifDec
PDFBibTeX XMLCite
Full Text: DOI

References:

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