The LFOPC leap-frog algorithm for constrained optimization

Abstract

This paper describes an accurate and reliable new algorithm (LFOPC) for solving constrained optimization problems, through a three-phase application of the well-established leap-frog method for unconstrained optimization, to penalty function formulations of the original constrained problems. The algorithm represents a considerable improvement over an earlier version (LFOPCON) which requires the judicious choice of parameter settings for efficient use. The current algorithm automatically executes normalization and scaling operations on the gradients of the constraints. This results in a robust algorithm that, apart from convergence tolerances, requires virtually no parameter settings. The method has been well tested, on both standard analytical test problems and practical engineering design problems.