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

Jacek Gondzio, Andreas Grothey
2006 Annals of Operations Research  
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.  ...  to be written for every type of problem separately.  ...  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

14th International Symposium on Mathematical Programming

1990 Mathematical programming  
If we use a decomposition approach in order to solve a minimization problem we often get an objective function in such a w a y that its domain dom 6 = n is not given explicitely to us.  ...  to the well known serious steps und null steps of bundle methods a third type of steps is used to generate the model of dom .  ...  The optimization solver is based on a sequential quadratic programming SQP method and treats convex quadratic subproblems with an interior point algorithm.  ... 
doi:10.1007/bf01580875 fatcat:3jtclwmntzgjxkqs5uecombdaa

QPLIB: a library of quadratic programming instances

Fabio Furini, Emiliano Traversi, Pietro Belotti, Antonio Frangioni, Ambros Gleixner, Nick Gould, Leo Liberti, Andrea Lodi, Ruth Misener, Hans Mittelmann, Nikolaos V. Sahinidis, Stefan Vigerske (+1 others)
2018 Mathematical Programming Computation  
, namely those for (4) parallel barrier solvers on large LP/QP problems, (5) AMPL-NLP and (6) MINLP.  ...  Actually, a slightly larger class of problems can be solved with Interior-Point methods: those that can be represented by Second-Order Cone Programs.  ...  The case for character strings is irrelevant.  ... 
doi:10.1007/s12532-018-0147-4 fatcat:7q7dunjewffb3ca2am6kmuf4im

OSQP: An Operator Splitting Solver for Quadratic Programs [article]

Bartolomeo Stellato, Goran Banjac, Paul Goulart, Alberto Bemporad, Stephen Boyd
2019 arXiv   pre-print
In addition, our technique is the first operator splitting method for quadratic programs able to reliably detect primal and dual infeasible problems from the algorithm iterates.  ...  We present a general purpose solver for convex quadratic programs based on the alternating direction method of multipliers, employing a novel operator splitting technique that requires the solution of  ...  We plan to add iterative indirect solvers and other direct solvers in future versions.  ... 
arXiv:1711.08013v3 fatcat:33o5es5nmndwncawsvsbfowzja

Recursive Direct Algorithms for Multistage Stochastic Programs in Financial Engineering [chapter]

Marc C. Steinbach
1999 Operations Research Proceedings 1998  
To exploit that structure, we propose a highly efficient dynamic programming recursion for the computationally intensive task of KKT systems solution within an interior point method.  ...  Multistage stochastic programs can be seen as discrete optimal control problems with a characteristic dynamic structure induced by the scenario tree.  ...  On the other hand, their structure is sufficiently general to catch the essentials of nonlinear stochastic optimization within interior point or sequential quadratic programming (SQP) methods.  ... 
doi:10.1007/978-3-642-58409-1_24 fatcat:tzz6nhbk4bbhzhf7xrg3y7pjji

Fast AC Power Flow Optimization using Difference of Convex Functions Programming [article]

Sandro Merkli and Alexander Domahidi and Juan Jerez and Manfred Morari and Roy S. Smith
2016 arXiv   pre-print
Traditionally, interior-point methods are used for solving the non-convex AC optimal power flow (OPF) problems arising in this type of simulation.  ...  Numerical results are presented comparing the method to state-of-the-art OPF solver implementations in MATPOWER, leading to significant speedups compared to the latter.  ...  Acknowledgments This work was supported by the Swiss Commission for Technology and Innovation (CTI), (Grant 16946.1 PFIW-IW).  ... 
arXiv:1602.02097v2 fatcat:ihlbjpnwobbanigmkypvljvida

A Semidefinite Programming Heuristic for Quadratic Programming Problems with Complementarity Constraints

Stephen Braun, John E. Mitchell
2005 Computational optimization and applications  
A quadratic programming problem is solved for each of these feasible solutions and the best resulting solution provides an estimate for the optimal solution to the quadratic program with complementarity  ...  A quadratic programming problem with complementarity constraints can be relaxed to give a semidefinite programming problem.  ...  Acknowledgements We would like to thank two anonymous referees for their constructive comments.  ... 
doi:10.1007/s10589-005-1014-6 fatcat:l3dmro46jvcatfcjtykcmxr3xu

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

Jacek Gondzio, Andreas Grothey
2007 European Journal of Operational Research  
Stochastic programming is recognized as a powerful tool to help decision making under uncertainty in financial planning.  ...  Interior point methods are well-suited to the solution of very large nonlinear optimization problems.  ...  Introduction Stochastic programming is recognized as an important tool in financial planning.  ... 
doi:10.1016/j.ejor.2006.03.006 fatcat:cojyxzpsszcp3gfqfeaart5nyy

Applications of reformulations in mathematical programming

Alberto Costa
2012 4OR  
This thesis is concerned with three mathematical programming applications where the reformulation was crucial to obtain a good solution.  ...  the original models but are somehow better (for instance in terms of computational time needed to obtain the solution by the solver).  ...  In 1984 Karmarkar proposed a better polynomial time interior point method to solve LP problems [139] .  ... 
doi:10.1007/s10288-012-0220-1 fatcat:47jmhf5adfg73joxngfmrsp44e

Challenges in the Application of Mathematical Programming in the Enterprise-wide Optimization of Process Industries

Ignacio E. Grossmann
2014 Теоретические основы химической технологии  
Procedure for Dynamic Multi-objective TSP Weiqi Li -Solving the vehicle routing problem with time windows by an interior point branch-price-and-cut framework Pedro Munari, Jacek Gondzio -A Parallel  ...  Barton Solving L1-CTA in 3D tables by an interior-point method for block-angular problems Jordi Cuesta, Jordi Castro 2 -Optimal Data-Independent Noise for Differential Privacy Josep Domingo-Ferrer, Jordi  ...  WA-29 Wednesday, 8:30-10:00 CC-A29 Data Mining Chair: Erik Kropat -Exact and heuristic algorithms based on Support Vector Machine for Feature Selection with application to Financial Problems Renato  ... 
doi:10.7868/s0040357114050054 fatcat:kli7aeuyxbaplfhup2t6nmuyxq

Advances in mathematical programming models for enterprise-wide optimization

Ignacio E. Grossmann
2012 Computers and Chemical Engineering  
Finally, based on the EWO program at the Center of Advanced Process Decision-making at Carnegie Mellon, we describe several applications to show the potential of this area.  ...  for remaining competitive in the global marketplace.  ...  Acknowledgment The author would like to acknowledge financial support from the member companies of the Center of Advanced Process Decision-making at Carnegie Mellon.  ... 
doi:10.1016/j.compchemeng.2012.06.038 fatcat:jxycpmzmpfa37kp4jh3artwvaa

Challenges in the application of mathematical programming in the enterprise-wide optimization of process industries

Ignacio E. Grossmann
2014 Theoretical foundations of chemical engineering  
Procedure for Dynamic Multi-objective TSP Weiqi Li -Solving the vehicle routing problem with time windows by an interior point branch-price-and-cut framework Pedro Munari, Jacek Gondzio -A Parallel  ...  Barton Solving L1-CTA in 3D tables by an interior-point method for block-angular problems Jordi Cuesta, Jordi Castro 2 -Optimal Data-Independent Noise for Differential Privacy Josep Domingo-Ferrer, Jordi  ...  WA-29 Wednesday, 8:30-10:00 CC-A29 Data Mining Chair: Erik Kropat -Exact and heuristic algorithms based on Support Vector Machine for Feature Selection with application to Financial Problems Renato  ... 
doi:10.1134/s0040579514050182 fatcat:3ra5yqooyzgmroo5qccbnauftm

Twenty years of linear programming based portfolio optimization

Renata Mansini, Wlodzimierz Ogryczak, M. Grazia Speranza
2014 European Journal of Operational Research  
The classical Markowitz model uses the variance as the risk measure and is a quadratic programming problem. Many attempts have been made to linearize the portfolio optimization problem.  ...  Several different risk measures have been proposed which are computationally attractive as (for discrete random variables) they give rise to linear programming (LP) problems.  ...  acknowledge the suggestions of two anonymous reviewers that have helped us to improve former versions of this paper.  ... 
doi:10.1016/j.ejor.2013.08.035 fatcat:de4gxfruenabncwqzw6oh5v7te

Modelling and solving environments for mathematical programming (MP): a status review and new directions

B Dominguez-Ballesteros, G Mitra, C Lucas, N-S Koutsoukis
2002 Journal of the Operational Research Society  
The interior point method for LP on parallel computers. In: Kall P (ed). Systems Modelling and Optimization. LNCIS180. Springer Verlag: Berlin, pp 241-250. Levkovitz R and Mitra G (1993).  ...  Such specialised applications comprise of user interface, database, optimisation models, and embedded solver tools customised for specific application domains, such as crew scheduling, supply chain planning  ... 
doi:10.1057/palgrave.jors.2601361 fatcat:brh5ag4uwrg33ltul2hvog2y2u

Exploiting structure in parallel implementation of interior point methods for optimization

Jacek Gondzio, Andreas Grothey
2008 Computational Management Science  
OOPS is an object oriented parallel solver using the primal-dual interior point methods.  ...  Gondzio, J & Grothey, A 2009 'Exploiting structure in parallel implementation of interior point methods for optimization, ' Computational Managment Science, vol. 6,  ...  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
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