Nonlinear Programming: Algorithms, Software, and Applications
K. Schittkowski, Ch. Zillober: in System Modeling and Optimization: Proceedings
of the 21st IFIP TC7 Conference held in July 21–25, 2003, Sophia
Antipolis, France, J. Cagnol, J.-P. Zolesio (eds.), Springer, Vol. 166, 73-108
We introduce some methods for constrained nonlinear programming that are widely used in practice and that are
known under the names SQP for sequential quadratic programming and SCP for sequential convex programming. In both cases, convex
subproblems are formulated, in the first case a quadratic programming problem, in the second case a separable
nonlinear program in inverse variables. The methods are outlined in a uniform way and the results of some comparative performance tests are listed.
We especially show the suitability of sequential convex programming methods to solve some classes of
very large scale nonlinear programs, where implicitly defined systems of equations seem to support the usage of inverse
approximations. The areas of interest are structural mechanical optimization, i.e., topology optimization, and optimal control of
partial differential equations after a full discretization. In addition, a few industrial applications and case studies are shown to illustrate practical situations
under which the codes implemented by the authors are in use.
To download a preprint, click here: nlp_rev.pdf