RPCGB Method for Large-Scale Global Optimization Problems

In this paper, we propose a new approach for optimizing a large-scale non-convex differentiable function subject to linear equality constraints. The proposed method, RPCGB (random perturbation of the conditional gradient method with bisection algorithm), computes a search direction by the conditiona...

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Bibliographic Details
Published in:Axioms Vol. 12; no. 6; p. 603
Main Authors: Ettahiri, Abderrahmane, El Mouatasim, Abdelkrim
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.06.2023
Subjects:
Algorithms
Approximation
bisection algorithm
conditional gradient method
Convex analysis
Cost function
Global optimization
large-scale problem
Linear programming
Mathematical optimization
Methods
non-convex optimization
Optimization techniques
Perturbation
random perturbation
Random variables
Signal processing
Stochastic processes
Morocco
ISSN:2075-1680, 2075-1680
Online Access:Get full text
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Summary:In this paper, we propose a new approach for optimizing a large-scale non-convex differentiable function subject to linear equality constraints. The proposed method, RPCGB (random perturbation of the conditional gradient method with bisection algorithm), computes a search direction by the conditional gradient, and an optimal line search is found by a bisection algorithm, which results in a decrease of the cost function. The RPCGB method is designed to guarantee global convergence of the algorithm. An implementation and testing of the method are given, with numerical results of large-scale problems that demonstrate its efficiency.
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ISSN:2075-1680
2075-1680
DOI:10.3390/axioms12060603