An interval sequential linear programming for nonlinear robust optimization problems

•An interval sequential linear programming for nonlinear robust optimization is proposed.•An approximate possibility sensitivity is proposed to efficiently obtain the partial derivatives of the constraints.•A novel iterative mechanism is established to improve the convergence rate.•Two numerical exa...

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Veröffentlicht in:Applied Mathematical Modelling Jg. 107; S. 256 - 274
Hauptverfasser: Tang, Jiachang, Fu, Chunming, Mi, Chengji, Liu, Haibo
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Elsevier Inc 01.07.2022
Elsevier BV
Schlagworte:
Interval uncertainty
Iterative methods
Linear programming
Optimization models
Reliability-based possibility degree of interval (RPDI)
Robust optimization
Robustness (mathematics)
Sensitivity analysis
Sequential linear programming
Interval uncertainty
Robust optimization
Sensitivity analysis
Sequential linear programming
Reliability-based possibility degree of interval (RPDI)
ISSN:0307-904X, 1088-8691, 0307-904X
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Zusammenfassung:•An interval sequential linear programming for nonlinear robust optimization is proposed.•An approximate possibility sensitivity is proposed to efficiently obtain the partial derivatives of the constraints.•A novel iterative mechanism is established to improve the convergence rate.•Two numerical examples and two practical engineering problems are applied to verify the accuracy and efficiency. In this paper, interval sequential linear programming (ISLP) is proposed to solve nonlinear robust optimization (RO). The main idea of the programming is to transform the uncertain optimization into several possibility-sensitivity analyses and deterministic linear optimization problems that are sequentially solved. At each cycle, a possibility-sensitivity analysis method is proposed to obtain the approximate partial derivatives of the uncertain constraints at the current design point, based on which a deterministic linear optimization model is constructed and the design point is updated by solving the linear optimization. Moreover, an iterative mechanism is created to adaptively update the design space and improve the convergence rate. Finally, two numerical examples and two practical engineering problems are applied to verify the accuracy and efficiency of the proposed method.
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ISSN:0307-904X
1088-8691
0307-904X
DOI:10.1016/j.apm.2022.02.037