A Method of Sequential Log-Convex Programming for Engineering Design

TL;DR

This paper introduces Sequential Log-Convex Programming (SLCP), a new method that leverages log-convex structures in engineering design problems, demonstrating significant efficiency improvements over existing methods.

Contribution

The paper develops SLCP, combining geometric programming with sequential quadratic programming, and demonstrates its effectiveness through test problems and integration with XFOIL for airfoil design.

Findings

SLCP reduces iteration count by up to 77% compared to SQP.

SLCP outperforms LSQP with an 11% reduction in iterations.

SLCP enables efficient evolution of design fidelity in engineering problems.

Abstract

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.