An Improved Spectral Conjugate Gradient Algorithm for Nonconvex Unconstrained Optimization Problems

AbstractA 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.

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A Spectral Dai-Yuan-Type Conjugate Gradient Method for Unconstrained Optimization

Mathematical Problems in Engineering ◽

10.1155/2015/839659 ◽

2015 ◽

Vol 2015 ◽

pp. 1-7

Author(s):

Guanghui Zhou ◽

Qin Ni

Keyword(s):

Unconstrained Optimization ◽

Conjugate Gradient Method ◽

Conjugate Gradient ◽

Gradient Method ◽

Large Scale ◽

Optimization Problems ◽

Sufficient Descent Condition ◽

Unconstrained Optimization Problems ◽

Spectral Conjugate Gradient ◽

Nonlinear Unconstrained Optimization

A new spectral conjugate gradient method (SDYCG) is presented for solving unconstrained optimization problems in this paper. Our method provides a new expression of spectral parameter. This formula ensures that the sufficient descent condition holds. The search direction in the SDYCG can be viewed as a combination of the spectral gradient and the Dai-Yuan conjugate gradient. The global convergence of the SDYCG is also obtained. Numerical results show that the SDYCG may be capable of solving large-scale nonlinear unconstrained optimization problems.

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A Modified Bat Algorithm with Conjugate Gradient Method for Global Optimization

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/2020/4795793 ◽

2020 ◽

Vol 2020 ◽

pp. 1-14

Author(s):

Huda I. Ahmed ◽

Eman T. Hamed ◽

Hamsa Th. Saeed Chilmeran

Keyword(s):

Conjugate Gradient ◽

Optimization Problems ◽

Statistical Tests ◽

Optimal Solution ◽

Bat Algorithm ◽

Conjugate Gradient Algorithm ◽

Gradient Algorithm ◽

Test Problems ◽

Spectral Conjugate Gradient ◽

Modified Bat Algorithm

Metaheuristic algorithms are used to solve many optimization problems. Firefly algorithm, particle swarm improvement, harmonic search, and bat algorithm are used as search algorithms to find the optimal solution to the problem field. In this paper, we have investigated and analyzed a new scaled conjugate gradient algorithm and its implementation, based on the exact Wolfe line search conditions and the restart Powell criterion. The new spectral conjugate gradient algorithm is a modification of the Birgin and Martínez method, a manner to overcome the lack of positive definiteness of the matrix defining the search direction. The preliminary computational results for a set of 30 unconstrained optimization test problems show that this new spectral conjugate gradient outperforms a standard conjugate gradient in this field and we have applied the newly proposed spectral conjugate gradient algorithm in bat algorithm to reach the lowest possible goal of bat algorithm. The newly proposed approach, namely, the directional bat algorithm (CG-BAT), has been then tested using several standard and nonstandard benchmarks from the CEC’2005 benchmark suite with five other algorithms and has been then tested using nonparametric statistical tests and the statistical test results show the superiority of the directional bat algorithm, and also we have adopted the performance profiles given by Dolan and More which show the superiority of the new algorithm (CG-BAT).

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