A Strictly Feasible Sequential
Convex Programming Method
S. Lehmann, K. Schittkowski, M. Stingl, F. Wein,
C. Zillober: submitted for publication (2013)
Abstract:
We propose a modification of a sequential convex programming (SCP) method
ensuring strict feasibility of objective and constraint function evaluations
subject to a given set of convex inequality constraints. The resulting procedure
is called feasible sequential convex programming method (FSCP). FSCP expands the
standard analytical subproblem of SCP methods, which is convex and separable, by
the nonlinear feasibility constraints. It is guaranteed that objective function
and remaining constraints are evaluated only at iterates which fulfill the
feasibility constraints. A line search based on an augmented Lagrangian merit
function is performed to guarantee global convergence, i.e., the approximation
of a KKT point. A case study is introduced, the numerical solution of free
material optimization (FMO) problems. Design variables are the material
properties represented by positive-semidefinite elasticity tensors based on a
given finite element discretization. The only restriction on the material is
that elasticity matrices remain positive definite throughout the algorithm, to
guarantee a positive definite global stiffness matrix. Some numerical results
are presented with up to 77,000 variables and 192,000 constraints.
To download the report, click here: feasSCP.pdf