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.
Organisations
People |
ORCID iD |
| Nicholas Ian Mark Gould (Principal Investigator) |
Publications
Gould N
(2015)
A Nonmonotone Filter SQP Method: Local Convergence and Numerical Results
in SIAM Journal on Optimization
Gould N
(2011)
How good are extrapolated bi-projection methods for linear feasibility problems?
in Computational Optimization and Applications
Gould N
(2010)
On solving trust-region and other regularised subproblems in optimization
in Mathematical Programming Computation
Gould N
(2010)
A Second Derivative SQP Method: Local Convergence and Practical Issues
in SIAM Journal on Optimization
Gould N
(2010)
Spectral Analysis of Saddle Point Matrices with Indefinite Leading Blocks
in SIAM Journal on Matrix Analysis and Applications
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
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
F. E. Curtis
(2014)
An interior-point trust-funnel algorithm for nonlinear optimization
Dollar H
(2010)
Preconditioning Saddle-Point Systems with Applications in Optimization
in SIAM Journal on Scientific Computing
Curtis F
(2015)
Adaptive augmented Lagrangian methods: algorithms and practical numerical experience
in Optimization Methods and Software
Cartis C
(2010)
On the Complexity of Steepest Descent, Newton's and Regularized Newton's Methods for Nonconvex Unconstrained Optimization Problems
in SIAM Journal on Optimization
Cartis C
(2009)
Trust-region and other regularisations of linear least-squares problems
in BIT Numerical Mathematics
Cartis C
(2009)
Adaptive cubic regularisation methods for unconstrained optimization. Part I: motivation, convergence and numerical results
in Mathematical Programming
Cartis C
(2010)
Adaptive cubic regularisation methods for unconstrained optimization. Part II: worst-case function- and derivative-evaluation complexity
in Mathematical Programming
Bellavia S
(2010)
Convergence of a Regularized Euclidean Residual Algorithm for Nonlinear Least-Squares
in SIAM Journal on 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/ |