A Sparse Superlinearly Convergent SQP with Applications to Two-dimensional Shape Optimization

Discretization of optimal shape design problems leads to very large nonlinear optimization problems. For attaining maximum computational efficiency, a sequential quadratic programming (SQP) algorithm should achieve superlinear convergence while preserving sparsity and convexity of the resulting quadratic programs. Most classical SQP approaches violate at least one of the requirements. We show that, for a very large class of optimization problems, one can design SQP algorithms that satisfy all these three requirements. The improvements in computational efficiency are demonstrated for a cam design problem. Address all correspondence to this author. The work of this author was supported by the Mathematical, Information and Computational Sciences Division subprogram of the Office of Computational and Technology Research, U.S. Department of Energy, under Contract W-31-109-Eng-38.