An accelerating outer space algorithm for globally solving generalized linear multiplicative problems

This paper proposes an accelerating outer space algorithm for globally solving generalized linear multiplicative problems (GLMP). Utilizing the logarithmic and exponential function properties, we begin with transforming the GLMP into an equivalent problem (EP) by introducing some outer space variabl...

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Bibliographic Details
Published in:Numerical algorithms Vol. 94; no. 2; pp. 877 - 904
Main Authors: Hou, Zhisong, Liu, Sanyang
Format: Journal Article
Language:English
Published: New York Springer US 01.10.2023
Springer Nature B.V
Subjects:
Algebra
Algorithms
Computer Science
Convergence
Exponential functions
Linear programming
Methods
Numeric Computing
Numerical Analysis
Original Paper
Relaxation method (mathematics)
Robustness (mathematics)
Theory of Computation
Variables
Global optimization
Accelerating outer space algorithm
Generalized linear multiplicative problems
Computational complexity
Branch-and-bound framework
ISSN:1017-1398, 1572-9265
Online Access:Get full text
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Summary:This paper proposes an accelerating outer space algorithm for globally solving generalized linear multiplicative problems (GLMP). Utilizing the logarithmic and exponential function properties, we begin with transforming the GLMP into an equivalent problem (EP) by introducing some outer space variables. Then, a two-stage outer space relaxation method is developed to convert the EP into a series of relaxed linear problems. Furthermore, to improve the convergence speed of the algorithm, we develop some accelerating techniques to remove the domains that do not contain a global optimal solution. Then, fusing the linear relaxed method and accelerating techniques into the branch-and-bound framework, we provide the accelerating outer space algorithm for solving the EP. Additionally, we analyze the global convergence of the proposed algorithm. Meanwhile, by investigating the algorithmic complexity, we estimate the maximum iterations required by the proposed algorithm in the worst case. Finally, in contrast to other algorithms in the currently known literature, numerical experimental results indicate that the proposed algorithm is feasible with better efficiency and robustness.
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ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-023-01523-y