Solution of Large Scale Optimization Problems with Sequential Convex Programming

The function g0 is the objective function of the problem, i.e. a cost function or a performance index that has to be minimized in order to have a better design. In topology optimization, this is for instance the compliance of the structure under the considered load case. The set of constraint functions gj (in number m) expresses the restrictions the design is subject to in order to be feasible. For example these functions are some bounds upon a stress measure to have resistance, restricted displacements, a volume resource or perimeter bound. . . The n variables xi are the design variables of the problem, that is, the parameters, which can be modified, to improve the design. In the topology optimization context, the xi variables are the element densities and the orientation parameters of the local microstructure. In optimization of composite structures, the xi variables may be the ply thicknesses