On the relaxation of constraints in a particular SQP algorithm

Dr. Tony Kearsley

Mathematical and Computational Sciences Division, National Institute of Standards and Technology, Gaithersburg, Maryland

In this talk, we will discuss a sequential quadratic programming (SQP) algorithm developed to solve general nonlinear programming (NLP) problems (minimization of a function subject to non-linear equality and inequality constraints). With an eye towards a particular class of application motivated problems, the algorithm solves a sequence of `relaxed' quadratic programming (QP) problems. The relaxation guarantees that the linearization of the constraints yields a consistent set of linear equations and thus the resulting relaxed QP is solvable. Numerical performance on a collection of test problems will show that inconsistent linearizations were encountered by the SQP algorithm and that the relaxation strategy appears to be effective at overcoming the difficulty. We conclude the talk with a short demonstration of the solution to one particular test problem (optimal control fluid flow).