Algorithms for Large-Scale Nonlinearly Constrained Optimization

The solution of large-scale nonlinear optimization-- minimization ormaximization - problems lies at the heart of scientificcomputation. Structures take up positions of minimal constrainedpotential energy, investors aim to maximize profit while controllingrisk, public utilities run transmission networks to satisfy demand atleast cost, and pharmaceutical companies desire minimal drug doses totarget pathogens. All of these problems are large either because themathematical model involves many parameters or because they are actuallyfinite discretisations of some continuous problem for which thevariables are functions.The purpose of this grant application is to support the design, analysisand development of new algorithms for nonlinear optimization that areparticularly aimed at the large-scale case.We shall focus on methods which attempt to improve simplified (cheaper) approximations of the actual (complicated) problem.Such a procedure may be applied recursively, and the mostsuccessful ideas in this vein are known as sequential quadraticprogramming (SQP). Our research is directed on ways to improve onSQP particularly when the underlying problem is large, and indeedparticularly in the case where SQP itself may be too expensive tocontemplate. The end goal of our research is to produce high-quality, publicly available software as part of the GALAHAD library.