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

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