Algorithms for Large-Scale Nonlinearly Constrained Optimization

Lead Research Organisation: University of Oxford
Department Name: Computer Science

Abstract

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.

Publications


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Gould N (2010) A Second Derivative SQP Method: Local Convergence and Practical Issues in SIAM Journal on Optimization
Gould N (2010) On solving trust-region and other regularised subproblems in optimization in Mathematical Programming Computation
Gould N (2010) Spectral Analysis of Saddle Point Matrices with Indefinite Leading Blocks in SIAM Journal on Matrix Analysis and Applications
Gould N (2011) How good are extrapolated bi-projection methods for linear feasibility problems? in Computational Optimization and Applications
Gould N (2015) A Nonmonotone Filter SQP Method: Local Convergence and Numerical Results in SIAM Journal on Optimization
Gould N (2010) A Second Derivative SQP Method: Global Convergence in SIAM Journal on Optimization
Gould N (2014) A Filter Method with Unified Step Computation for Nonlinear Optimization in SIAM Journal on Optimization
Gould N (2008) Nonlinear programming without a penalty function or a filter in Mathematical Programming
Gould N (2011) A second-derivative SQP method with a 'trust-region-free' predictor step in IMA Journal of Numerical Analysis
 
Description We have designed, analysed and implemented a variety of novel algorithms for solving nonlinear optimization (minimization or maximization) problems. Such problems arise throught science, engineering, economics and planning, and are at the heart of human enterprise.
Exploitation Route The essential algorithms we have developed form part of GALAHAD, our library of packages for solving nonlinear optimization problems.
The theoretical implications are available to all via our publications,
and have moved forward our understanding of how optimization methods work.
Sectors Aerospace, Defence and Marine,Chemicals,Construction,Digital/Communication/Information Technologies (including Software),Education,Electronics,Energy,Environment,Manufacturing, including Industrial Biotechology,Pharmaceuticals and Medical Biotechnology,Retail,Transport,Other
URL http://www.numerical.rl.ac.uk/people/nimg/
 
Description The open source optimization packages GALAHAD and CUTEst have been dowloaded by a variety of academic and commercial organisations.
First Year Of Impact 2005
Sector Aerospace, Defence and Marine,Chemicals,Construction,Education,Energy,Transport,Other
Impact Types Economic
 
Title GALAHAD 
Description A library of packages for nonlinear optimization 
Type Of Technology Software 
Year Produced 2006 
Open Source License? Yes  
Impact Downloaded more than 1000 times 
URL http://www.galahad.rl.ac.uk/