  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.
