Globally convergent algorithms for solving unconstrained optimization problems

A modified spectral methods for solving unconstrained optimization problems based on the formulae are derived which are given in [4, 5]. The proposed methods satisfied the descent condition. Moreover, we prove that the new spectral methods are globally convergent. The Numerical results show that the proposed methods effective by comparing with the FR-method.

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MULTIPLE USE OF BACKTRACKING LINE SEARCH IN UNCONSTRAINED OPTIMIZATION

Facta Universitatis Series Mathematics and Informatics ◽

10.22190/fumi2005417i ◽

2021 ◽

pp. 1417

Author(s):

Branislav Ivanov ◽

Bilall I. Shaini ◽

Predrag S. Stanimirović

Keyword(s):

Unconstrained Optimization ◽

Line Search ◽

Optimization Problems ◽

Multiple Use ◽

Computationally Efficient ◽

Performance Profiling ◽

Unconstrained Optimization Problems ◽

Globally Convergent ◽

Backtracking Line Search ◽

And Performance

The gradient method is a very efficient iterative technique for solving unconstrained optimization problems. Motivated by recent modifications of some variants of the SM method, this study proposed two methods that are globally convergent as well as computationally efficient. Each of the methods is globally convergent under the influence of a backtracking line search. Results obtained from the numerical implementation of these methods and performance profiling show that the methods are very competitive with well-known traditional methods.

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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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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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