Modified Courant-Beltrami penalty function and its convergence

A Courant-Beltrami penalty function is the square of the absolute value penalty function for inequality constraints, and it penalizes any violations of the constraints function gi(x) ≤ 0 but does not prevent such violations. In this paper, we modified a Courant-Beltrami penalty function method for s...

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Bibliographic Details
Main Authors: Hassan, Mansur, Baharum, Adam
Format: Conference Proceeding
Language:English
Subjects:
Algorithms
Constraints
Convergence
Mathematical programming
Nonlinear programming
Optimization
Penalty function
Queuing theory
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Summary:A Courant-Beltrami penalty function is the square of the absolute value penalty function for inequality constraints, and it penalizes any violations of the constraints function gi(x) ≤ 0 but does not prevent such violations. In this paper, we modified a Courant-Beltrami penalty function method for solving constrained nonlinear programming problems. The results obtained indicate that the modified Courant-Beltrami (MCB) penalty function method provides the approximate optimal solutions and improved objective value using a fixed penalty parameter. Moreover, we investigate and proved MCB penalty function convergence, which has been supported by some numerical test examples. Furthermore, a quasi-newton algorithm was adopted to implement the result on MATLAB2018a via routine function fminunc for unconstrained optimization, the results have shown that the MCB penalty function method converges to a local minimum faster than the existing Courant-Beltrami penalty function method.
ISSN:0094-243X
1551-7616
DOI:10.1063/1.5136374