A sequential adaptive regularisation using cubics algorithm for solving nonlinear equality constrained optimization

The adaptive regularisation algorithm using cubics (ARC) is initially proposed for unconstrained optimization. ARC has excellent convergence properties and complexity. In this paper, we extend ARC to solve nonlinear equality constrained optimization and propose a sequential adaptive regularisation u...

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Bibliographic Details
Published in:Computational optimization and applications Vol. 84; no. 3; pp. 1005 - 1033
Main Authors: Pei, Yonggang, Song, Shaofang, Zhu, Detong
Format: Journal Article
Language:English
Published: New York Springer US 01.04.2023
Springer Nature B.V
Subjects:
Adaptive algorithms
Algorithms
Convergence
Convex and Discrete Geometry
Iterative methods
Management Science
Mathematics
Mathematics and Statistics
Operations Research
Operations Research/Decision Theory
Optimization
Penalty function
Quadratic programming
Reduction
Regularization
Statistics
Global convergence
65K05
90C30
Adaptive regularization with cubics
Nonlinear optimization
65K10
49M37
Constrained optimization
ISSN:0926-6003, 1573-2894
Online Access:Get full text
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Summary:The adaptive regularisation algorithm using cubics (ARC) is initially proposed for unconstrained optimization. ARC has excellent convergence properties and complexity. In this paper, we extend ARC to solve nonlinear equality constrained optimization and propose a sequential adaptive regularisation using cubics algorithm inspired by sequential quadratic programming (SQP) methods. In each iteration of our method, the trial step is computed via composite-step approach, i.e., it is decomposed into the sum of normal step and tangential step. By means of reduced-Hessian approach, a new ARC subproblem for nonlinear equality constrained optimization is constructed to compute the tangential step, which can supply sufficient decrease required in the proposed algorithm. Once the trial step is obtained, the ratio of the penalty function reduction to the model function reduction is calculated to determine whether the trial point is accepted. The global convergence of the algorithm is investigated under some mild assumptions. Preliminary numerical experiments are reported to show the performance of the proposed algorithm.
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ISSN:0926-6003
1573-2894
DOI:10.1007/s10589-022-00449-w