Sequential Convex Programming Methods

Sequential convex programming methods became very popular in the past for special domains of application, e.g. the optimal structural design in mechanical engineering. The algorithm uses an inverse approximation of certain variables so that a convex, separable nonlinear programming problem must be solved in each iteration. In this paper the method is outlined and it is shown, how the iteration process can be stabilized by a line search. The convergence results are presented for a special variant called method of moving asymptotes. The algorithm was implemented in FORTRAN and the numerical performance is evaluated by a comparative study, where the test problems are formulated through a finite element analysis.