Positive Definiteness of Symmetric Rank 1 (H-Version) Update for Unconstrained Optimization

In this work we propose and analyze a hybrid conjugate gradient (CG) method in which the parameter is computed as a linear combination between Hager-Zhang [HZ] and Dai-Liao [DL] parameters. We use this proposed method to modify BFGS method and to prove the positive definiteness and QN-conditions of the matrix. Theoretical trils confirm that the new search directions aredescent directions under some conditions, as well as, the new search directions areglobally convergent using strong Wolfe conditions. The numerical experiments show that the proposed method is promising and outperforms alternative similar CG-methods using Dolan-Mor'e performance profile.

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A NEW SPECTRAL PARAMETER GRADIENT VECTOR THAT SATISFIED WEAK SECANT EQUATION FOR SOLVING LARGE SCALE UNCONSTRAINED OPTIMIZATION

Advances in Mathematics: Scientific Journal ◽

10.37418/amsj.10.1.6 ◽

2020 ◽

Vol 10 (1) ◽

pp. 1857-8365

Author(s):

M. I. Ishak ◽

S. M. Marjugi ◽

L. W. June

Keyword(s):

Unconstrained Optimization ◽

Spectral Parameter ◽

Large Scale ◽

Gradient Vector ◽

Secant Equation ◽

Large Scale Unconstrained Optimization ◽

Parameter Gradient

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A MODIFIED BFGS METHOD VIA NEW RATIONAL APPROXIMATION MODEL FOR SOLVING UNCONSTRAINED OPTIMIZATION PROBLEMS AND ITS APPLICATION

Advances in Mathematics: Scientific Journal ◽

10.37418/amsj.9.12.61 ◽

2020 ◽

Vol 9 (12) ◽

pp. 10771-10786

Author(s):

K. Kamfa ◽

S. Ibrahim ◽

S. F. Sufahani ◽

R. B. Yunus ◽

M. Mamat

Keyword(s):

Unconstrained Optimization ◽

Rational Approximation ◽

Optimization Problems ◽

Bfgs Method ◽

Approximation Model ◽

Unconstrained Optimization Problems

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Tensor Methods for Unconstrained Optimization Using Second Derivatives

10.21236/ada213642 ◽

1989 ◽

Cited By ~ 2

Author(s):

Robert B. Schnabel ◽

Ta-Tung Chow

Keyword(s):

Unconstrained Optimization ◽

Tensor Methods ◽

Second Derivatives

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A Software Package for Unconstrained Optimization Using Tensor Methods

10.21236/ada233989 ◽

1990 ◽

Author(s):

Ta-Tung Chow ◽

Elizabeth Eskow ◽

Robert B. Schnabel

Keyword(s):

Unconstrained Optimization ◽

Software Package ◽

Tensor Methods

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A Non-Monotone Line Search Combination Technique for Unconstrained Optimization

The Open Electrical & Electronic Engineering Journal ◽

10.2174/1874129001408010218 ◽

2014 ◽

Vol 8 (1) ◽

pp. 218-221 ◽

Cited By ~ 2

Author(s):

Ping Hu ◽

Zong-yao Wang

Keyword(s):

Global Convergence ◽

Unconstrained Optimization ◽

Numerical Experiments ◽

Line Search ◽

Optimization Problems ◽

Search Algorithm ◽

New Combination ◽

Combination Rule ◽

Combination Technique ◽

Unconstrained Optimization Problems

We propose a non-monotone line search combination rule for unconstrained optimization problems, the corresponding non-monotone search algorithm is established and its global convergence can be proved. Finally, we use some numerical experiments to illustrate the new combination of non-monotone search algorithm’s effectiveness.

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