A New Adaptive Conjugate Gradient Algorithm for Large-Scale Unconstrained Optimization

Neculai Andrei ()
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Neculai Andrei: Research Institute for Informatics

A chapter in Optimization and Its Applications in Control and Data Sciences, 2016, pp 1-16 from Springer

Abstract: Abstract An adaptive conjugate gradient algorithm is presented. The search direction is computed as the sum of the negative gradient and a vector determined by minimizing the quadratic approximation of objective function at the current point. Using a special approximation of the inverse Hessian of the objective function, which depends by a positive parameter, we get the search direction which satisfies both the sufficient descent condition and the Dai-Liao’s conjugacy condition. The parameter in the search direction is determined in an adaptive manner by clustering the eigenvalues of the matrix defining it. The global convergence of the algorithm is proved for uniformly convex functions. Using a set of 800 unconstrained optimization test problems we prove that our algorithm is significantly more efficient and more robust than CG-DESCENT algorithm. By solving five applications from the MINPACK-2 test problem collection, with 106 variables, we show that the suggested adaptive conjugate gradient algorithm is top performer versus CG-DESCENT.

Keywords: Unconstrained optimization; Adaptive conjugate gradient method; Sufficient descent condition; Conjugacy condition; Eigenvalues clustering; Numerical comparisons (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/978-3-319-42056-1_1

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