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Exploiting structure in parallel implementation of interior point methods for optimization

Jacek Gondzio, Andreas Grothey
2008 Computational Management Science  
Gondzio, J & Grothey, A 2009 'Exploiting structure in parallel implementation of interior point methods for optimization, ' Computational Managment Science, vol. 6,  ...  OOPS is an object oriented parallel solver using the primal-dual interior point methods.  ...  Linear Algebra in Interior Point Methods Interior point methods provide a unified framework for optimization algorithms for linear, quadratic and nonlinear programming.  ... 
doi:10.1007/s10287-008-0090-3 fatcat:ogkohifljbfvjmr32winnntuvi

Parallel interior-point solver for structured linear programs

Jacek Gondzio, Robert Sarkissian
2003 Mathematical programming  
Issues of implementation of an object-oriented library for parallel interior-point methods are addressed. The solver can easily exploit any special structure of the underlying optimization problem.  ...  In particular, it allows a nested embedding of structures and by this means very complicated real-life optimization problems can be modelled.  ...  Acknowledgements We are grateful to Ken McKinnon for his careful reading of the paper and his insightful comments, and to Andreas Grothey for help in running the parallel version of the solver.  ... 
doi:10.1007/s10107-003-0379-5 fatcat:6sj54wj6pfhaxmdfzbf62zw4bq

Direct Solution of Linear Systems of Size 109 Arising in Optimization with Interior Point Methods [chapter]

Jacek Gondzio, Andreas Grothey
2006 Lecture Notes in Computer Science  
A parallel implementation of an interior point method is described in this paper. It uses object-oriented programming techniques and allows for exploiting different block-structures of matrices.  ...  Solution methods for very large scale optimization problems are addressed in this paper. Interior point methods are demonstrated to provide unequalled efficiency in this context.  ...  Acknowledgements We are grateful to the EPCC for allowing us to use the BlueGene service and to Dr Joachim Hein in particular for his help in running OOPS on this machine.  ... 
doi:10.1007/11752578_62 fatcat:oj4sszgopfdexh3iurlfbvro2y

An annotated bibliography of network interior point methods

Mauricio G. C. Resende, Geraldo Veiga
2003 Networks  
We consider single and multicommodity network flow problems, as well as preconditioners used in implementations of conjugate gradient methods for solving the normal systems of equations that arise in interior  ...  This paper presents an annotated bibliography on interior point methods for solving network flow problems.  ...  Others exploit the special structure of network flow problems to speedup the computation of interior point methods.  ... 
doi:10.1002/net.10087 fatcat:zwiupodkbbhkrmhm34cxpol4cu

Model predictive control for deeply pipelined field-programmable gate array implementation: algorithms and circuitry

J.L. Jerez, E.C. Kerrigan, G.A. Constantinides, K.-V. Ling
2012 IET Control Theory & Applications  
The focus is on exploiting the structure and accelerating the computational bottleneck in an existing primal-dual interior-point method.  ...  In this paper we present a parameterized field-programmable gate array (FPGA) implementation of a customized QP solver for optimal control of linear processes with constraints, which can achieve substantial  ...  ACKNOWLEDGMENT The authors would like to acknowledge the support of the EPSRC (Grant EP/G031576/1), discussions with Prof. Jan Maciejowski, Mr. David Boland and Mr.  ... 
doi:10.1049/iet-cta.2010.0441 fatcat:wpf4rkvaajg25dhmrswzznazfu

Parallel interior-point solver for structured quadratic programs: Application to financial planning problems

Jacek Gondzio, Andreas Grothey
2006 Annals of Operations Research  
A reformulation of the problem is proposed which reduces density of matrices involved and by these means significantly simplifies its solution by an interior point method.  ...  We present a linear algebra library tailored for problems with such structure that is used inside an interior point solver for convex quadratic programming problems.  ...  Acknowledgements We are grateful to the anonymous referees for constructive comments, resulting in an improved presentation.  ... 
doi:10.1007/s10479-006-0139-z fatcat:23wnhcuxtrdoraiiaayw62dwxi

On Exploiting Problem Structure in a Basis Identification Procedure for Linear Programming

Erling D. Andersen
1999 INFORMS journal on computing  
However, in many practical applications of LP, interior-point methods have the drawback that they do not generate an optimal basic and nonbasic partition of the variables.  ...  During the last decade interior-point methods have become an e cient alternative to the simplex algorithm for solution of large-scale linear programming (LP) problems.  ...  In each iteration of a primal-dual interior-point method, a guess (x;ŷ;ŝ) 2 R n ++ R m R n ++ for the primal and dual optimal solution is generated.  ... 
doi:10.1287/ijoc.11.1.95 fatcat:qtpa64gukrefnhux7xrwy3ysv4

Exploiting hardware capabilities in interior point methods

Csaba Mészáros
2015 Optimization Methods and Software  
We investigate how the recently introduced Advanced Vector Instruction (AVX) set on Intel-compatible architectures can be exploited in interior point methods for linear and nonlinear optimization.  ...  We focus on data structures and implementation techniques that utilize the new vector instructions.  ...  Introduction Interior point methods (IPMs) have proved to be efficient tools in practice for solving large-scale optimization problems [9, 3] .  ... 
doi:10.1080/10556788.2015.1104677 fatcat:cyh5bfhu7vacnd2uegnmztv2qu

On parallelizing dual decomposition in stochastic integer programming

Miles Lubin, Kipp Martin, Cosmin G. Petra, Burhaneddin Sandıkçı
2013 Operations Research Letters  
We address an important bottleneck of parallel execution by identifying a formulation that permits the parallel solution of the master program by using structure-exploiting interior-point solvers.  ...  Our results demonstrate the potential for parallel speedup and the importance of regularization (stabilization) in the dual optimization.  ...  Block-angular structure in linear and quadratic programs has been successfully exploited for parallelization within interior-point methods [25, 26] .  ... 
doi:10.1016/j.orl.2013.02.003 fatcat:7ftwqcfwobgnjjv5qje2xwwkhq

Solving non-linear portfolio optimization problems with the primal-dual interior point method

Jacek Gondzio, Andreas Grothey
2007 European Journal of Operational Research  
Interior point methods are well-suited to the solution of very large nonlinear optimization problems.  ...  In this paper we exploit this feature and show how portfolio optimization problems with sizes measured in millions of constraints and decision variables, featuring constraints on semi-variance, skewness  ...  Such nested block-structures can be exploited by modern implementations of interior point methods such as OOPS [6] .  ... 
doi:10.1016/j.ejor.2006.03.006 fatcat:cojyxzpsszcp3gfqfeaart5nyy

Parallel Exploitation for Tree-Structured Coupled Quadratic Programming in Julia

Shervin Parvini Ahmadi, Anders Hansson
2018 2018 22nd International Conference on System Theory, Control and Computing (ICSTCC)  
The main idea in this paper is to implement a distributed primal-dual interior-point algorithm for loosely coupled Quadratic Programming problems.  ...  We implement this in Julia and show how can we exploit parallelism in order to increase the computational speed. We investigate the performance of the algorithm on a Model Predictive Control problem.  ...  The authors are grateful for discussions with Sina Khoshfetrat Pakazad and Erik Hedberg.  ... 
doi:10.1109/icstcc.2018.8540646 fatcat:giw6fuww6jgnbivdtb74rwuet4

An FPGA implementation of a sparse quadratic programming solver for constrained predictive control

Juan Luis Jerez, George Anthony Constantinides, Eric C. Kerrigan
2011 Proceedings of the 19th ACM/SIGDA international symposium on Field programmable gate arrays - FPGA '11  
We present a high-throughput floating-point FPGA implementation that exploits the parallelism inherent in interior-point optimization methods.  ...  The implementation yields a 6.5x improvement in latency and a 51x improvement in throughput for large problems over a software implementation running on a general purpose microprocessor.  ...  ACKNOWLEDGMENTS The authors would like to acknowledge the support of the EPSRC (Grant EP/G031576/1), discussions with Prof. Jan Maciejowski, Prof. Ling Keck Voon, Mr. David Boland and Mr.  ... 
doi:10.1145/1950413.1950454 dblp:conf/fpga/JerezCK11 fatcat:rwl7ifuocjhhvldvi3norsns6e

Optimizing Large-Scale Linear Energy System Problems with Block Diagonal Structure by Using Parallel Interior-Point Methods [chapter]

Thomas Breuer, Michael Bussieck, Karl-Kiên Cao, Felix Cebulla, Frederik Fiand, Hans Christian Gils, Ambros Gleixner, Dmitry Khabi, Thorsten Koch, Daniel Rehfeldt, Manuel Wetzel
2018 Operations Research Proceedings  
A key aspect are extensions to the parallel interior-point solver PIPS-IPM originally developed for stochastic optimization problems.  ...  This article describes an interdisciplinary approach to exploit the intrinsic structure of these large-scale linear problems to be able to solve them on massively parallel high-performance computers.  ...  Ambros Gleixner was supported by the Research Campus MODAL Mathematical Optimization and Data Analysis Laboratories funded by the Federal Ministry of Education and Research (BMBF Grant 05M14ZAM).  ... 
doi:10.1007/978-3-319-89920-6_85 dblp:conf/or/BreuerBCCFGGKKR17 fatcat:2noqq3bkcbasvjety2vwbjdqqa

Hybrid MPI/OpenMP Parallel Linear Support Vector Machine Training

Kristian Woodsend, Jacek Gondzio
2009 Journal of machine learning research  
Using an interior point method for the optimization and a reformulation that avoids the dense Hessian matrix, the structure of the augmented system matrix is exploited to partition data and computations  ...  A parallel implementation of linear Support Vector Machine training has been developed, using a combination of MPI and OpenMP.  ...  This work has made use of the resources provided by the  ... 
dblp:journals/jmlr/WoodsendG09 fatcat:lxnpmdxdyraldl6xugvhfr5uuu

Graph Cuts via $\ell_1$ Norm Minimization

A. Bhusnurmath, C.J. Taylor
2008 IEEE Transactions on Pattern Analysis and Machine Intelligence  
The proposed procedure exploits the structure of these linear systems in a manner that is easily amenable to parallel implementations.  ...  In this paper, the graph cut problem is reformulated as an unconstrained ' 1 norm minimization that can be solved effectively using interior point methods.  ...  In all cases, the implementation converges in less than 15 Newton steps, which is consistent with the observed performance of interior point methods.  ... 
doi:10.1109/tpami.2008.82 pmid:18703837 fatcat:wkngxrhvxnb3piylyvdxl76eze
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