A method of sequential log-convex programming for engineering design

A method of Sequential Log-Convex Programming (SLCP) is constructed that exploits the log-convex structure present in many engineering design problems. The mathematical structure of Geometric Programming (GP) is combined with the ability of Sequential Quadratic Program (SQP) to accommodate a wide ra...

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Bibliographic Details
Published in:Optimization and engineering 2023-09, Vol.24 (3), p.1719-1745
Main Authors: Karcher, Cody, Haimes, Robert
Format: Article
Language:English
Subjects:
Algorithms
Computational geometry
Control
Convexity
Design engineering
Engineering
Environmental Management
Financial Engineering
Mathematical programming
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Quadratic programming
Reduction
Research Article
Systems Theory
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Summary:A method of Sequential Log-Convex Programming (SLCP) is constructed that exploits the log-convex structure present in many engineering design problems. The mathematical structure of Geometric Programming (GP) is combined with the ability of Sequential Quadratic Program (SQP) to accommodate a wide range of objective and constraint functions, resulting in a practical algorithm that can be adopted with little to no modification of existing design practices. Three test problems are considered to demonstrate the SLCP algorithm, comparing it with SQP and the modified Logspace Sequential Quadratic Programming (LSQP). In these cases, SLCP shows up to a 77% reduction in number of iterations compared to SQP, and an 11% reduction compared to LSQP. The airfoil analysis code XFOIL is integrated into one of the case studies to show how SLCP can be used to evolve the fidelity of design problems that have initially been modeled as GP compatible. Finally, a methodology for design based on GP and SLCP is briefly discussed.
ISSN:1389-4420
1573-2924
DOI:10.1007/s11081-022-09750-3