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A Deterministic Linear Program Solver in Current Matrix Multiplication Time [article]

Jan van den Brand
2020 arXiv   pre-print
More accurately we are able to maintain √(U)A^(AUA^)^-1A√(U) v in subquadratic time under ℓ_2 multiplicative changes to the diagonal matrix U and the vector v.  ...  Their algorithm can solve linear programs in Õ(n^ωlog(n/δ)) expected time, where δ is the relative accuracy.  ...  The algorithmic descriptions in this paper use latex-code of [CLS18] , available under CC-BY-4.0 10  ... 
arXiv:1910.11957v2 fatcat:ms73j6qbezghndyra756bmzxvi

Erasure coding for fault oblivious linear system solvers [article]

David F. Gleich and Ananth Grama and Yao Zhu
2014 arXiv   pre-print
We demonstrate this approach on the problem of solving sparse linear systems using a conjugate gradient solver. We present input augmentation and output recovery techniques.  ...  Specifically, we demonstrate cases where a single fault can be corrected with less than 10% overhead in time, and even in extreme cases (fault rates of 20%), our approach is able to compute a solution  ...  In the presence of a substantial number of faults (20% of components failing), it takes 5 times the number of iterations of a linear solver.  ... 
arXiv:1412.7364v1 fatcat:3jqqcudqf5hrfkmev63hva5qre

Robust and Scalable Power System State Estimation via Composite Optimization [article]

Gang Wang and Georgios B. Giannakis and Jie Chen
2019 arXiv   pre-print
However, due to nonconvexity and nonsmoothness, existing LAV solvers based on linear programming are typically slow, hence inadequate for real-time system monitoring.  ...  The first is a deterministic linear proximal scheme that handles a sequence of convex quadratic problems, each efficiently solvable either via off-the-shelf algorithms or through the alternating direction  ...  DETERMINISTIC PROX-LINEAR LAV SOLVER In this section, we will develop a deterministic solver of (7) .  ... 
arXiv:1708.06013v2 fatcat:hbpfdiunsjbi5owk2tte6uyk4e

FPGA implementation of an interior point solver for linear model predictive control

Juan L. Jerez, George A. Constantinides, Eric C. Kerrigan
2010 2010 International Conference on Field-Programmable Technology  
The main hurdle is the need to solve a computationally intensive quadratic programming (QP) problem in real-time.  ...  This work builds on a previous FPGA implementation of an iterative linear solver, an operation at the heart of the interior-point method.  ...  computing this matrix-vector multiplication in a row-by-row fashion.  ... 
doi:10.1109/fpt.2010.5681439 dblp:conf/fpt/JerezCK10 fatcat:coepjv6ijfdtbhewaz4fhx32fu

Financial Portfolio Optimization: Computationally guided agents to investigate, analyse and invest!? [article]

Ankit Dangi
2013 arXiv   pre-print
using a decision matrix for neighbourhood generation.  ...  Conceptual understanding of classes of solver agents that represent varying problem formulations and, mathematically oriented deterministic solvers along with stochastic-search driven evolutionary and  ...  The super-agent solver may be a stochastic-search solver or a deterministic solver with multiple starting points.  ... 
arXiv:1301.4194v1 fatcat:xjh7x3tglbgh5eggl7zz3rzs74

Enhancing Monte Carlo Preconditioning Methods for Matrix Computations

Janko Straßburg, Vassil Alexandrov
2014 Procedia Computer Science  
This method is used in contrast to the standard deterministic preconditioners computed by the deterministic SPAI, and its further optimized parallel variant-Modified SParse Approximate Inverse Preconditioner  ...  The advantage of this approach is that we use sparse Monte Carlo matrix inversion whose computational complexity is linear of the size of the matrix.  ...  Introduction Solving systems of linear algebraic equations (SLAE) in the form of Ax = b or inverting a real matrix A is of unquestionable importance in many scientific and engineering applications.  ... 
doi:10.1016/j.procs.2014.05.143 fatcat:5luky3xb3fex5ojs4hykuuncwy

Fault-tolerant linear solvers via selective reliability [article]

Patrick G. Bridges, Kurt B. Ferreira, Michael A. Heroux, Mark Hoemmen
2012 arXiv   pre-print
Using this framework, we wrote a fault-tolerant iterative linear solver using components from the Trilinos solvers library. Our solver exploits hybrid parallelism (MPI and threads).  ...  Furthermore, they store most of their data unreliably, and spend most of their time in unreliable mode.  ...  Acknowledgment This work was supported in part by a faculty sabbatical appointment from Sandia National Laboratories and a grant from the U.S. Department of Energy and  ... 
arXiv:1206.1390v1 fatcat:ttowhmggzrbb5hsawtvli7pgue

Portfolio optimization: New capabilities and future methods

Ralph E. Steuer, Yue Qi, Markus Hirschberger
2006 Zeitschrift für Betriebswirtschaft  
Another is that MPQ runs in reasonable time with dense covariance matrices thus obviating the need in many cases to diagonalize the covariance matrix structure for CPU-time purposes.  ...  The computer capability is designated MPQ (for multi-parametric quadratic programming) and has been programmed in Java. • MPQ possesses several advantages.  ...  more linear objectives, equivalent deterministic implementation programs can become difficult.  ... 
doi:10.1007/s11573-006-0006-z fatcat:fic7skthb5d7vdqonimkg5tbiq

SLP-IOR: An interactive model management system for stochastic linear programs

Peter Kall, János Mayer
1996 Mathematical programming  
In this paper stochastic linear programming (SLP) is considered from the model management point of view.  ...  The central topic of the paper is SLP-IOR itself which is a model management system for SLP being under development by the authors.  ...  Let us remark that there does not exist a general SLP solver, like the implementations of the simplex method in linear programming.  ... 
doi:10.1007/bf02592153 fatcat:jjabjryi7rhnbmfwkf27lnsg7y

A Fast Binary Quadratic Programming Solver based on Stochastic Neighborhood Search

Benson S.Y. Lam, Alan Liew
2020 IEEE Transactions on Pattern Analysis and Machine Intelligence  
In this paper, we propose a BQP solver that alternatingly applies a deterministic search and a stochastic neighborhood search.  ...  Current methodologies either adopt an independent random search in a semi-definite space or perform search in a relaxed biconvex space.  ...  ACKNOWLEDGMENT The work described in this paper was partially supported by the grants from Research Grants Council of the Hong Kong Special Administrative Region, China (Project No.  ... 
doi:10.1109/tpami.2020.3010811 pmid:32750824 fatcat:dm6ssuozdnel3lc3gxoujbpymi

Stable implementation of a deterministic multi-subband Boltzmann solver for Silicon Double-Gate nMOSFETs

Kai Zhao, Sung-Min Hong, Christoph Jungemann, Ru-Qi Han
2010 2010 International Conference on Simulation of Semiconductor Processes and Devices  
Silicon Double Gate nMOSFETs are simulated using a deterministic Boltzmann solver coupled with a 1D Schrödinger and 2D Poisson Equation.  ...  Subthreshold characteristics and high drain bias conditions can be well simulated by the solver stabilized by the H-transformation and the maximum entropy dissipation scheme.  ...  Filling the Jacobian matrix and solving the BTE consumes the largest part of the CPU time, where the total CPU time for one bias point is 5h or less on a single CPU core and the memory requirement a few  ... 
doi:10.1109/sispad.2010.5604500 fatcat:gp35jxkes5btxpd5x7busouyi4

Tiresias

Alexandra Meliou, Dan Suciu
2012 Proceedings of the 2012 international conference on Management of Data - SIGMOD '12  
Figure 3 : Example query Q 2 : A TiQL program that deletes line items in order to achieve a desired KPI. HTABLES: HChooseS(ok,pk,sk,sk')  ...  Mixed Integer Programming problems, on top of a relational database system.  ...  That approach also translates the problem into a Linear Program and uses an LP solver to compute a solution.  ... 
doi:10.1145/2213836.2213875 dblp:conf/sigmod/MeliouS12 fatcat:v37orjkbpzgz5hqynjmqviztxq

Optimal power flow: a bibliographic survey I

Stephen Frank, Ingrida Steponavice, Steffen Rebennack
2012 Energy Systems, Springer Verlag  
In this two-part survey, we survey both the classical and recent OPF literature in order to provide a sound context for the state of the art in OPF formulation and solution methods.  ...  Part II of the survey examines the recent trend towards stochastic, or non-deterministic, search techniques and hybrid methods for OPF.  ...  However, because the linear program is constructed around a current operating point, these methods find local optima only.  ... 
doi:10.1007/s12667-012-0056-y fatcat:icsiux73qvffrh3mxxnutpsg54

Valuing programs with deterministic and stochastic cycles

Harry J. Paarsch, John Rust
2009 Journal of Economic Dynamics and Control  
In many dynamic programming problems, a mix of state variables exists -some exhibiting stochastic cycles and others having deterministic cycles.  ...  Our strategy for computing the left-inverse of the matrix ½I À bP, which is central to implementing Howard's policy iteration algorithm, yields significant improvements in computation time and major reductions  ...  The ideas contained in this paper represent the views of the authors and do not reflect the views of the National Science Foundation or the British Columbia Ministry of Forests and Range.  ... 
doi:10.1016/j.jedc.2008.08.007 fatcat:qspldmc55beldlz6hakrv23e5q

A multi-core high performance computing framework for probabilistic solutions of distribution systems

Tao Cui, F. Franchetti
2012 2012 IEEE Power and Energy Society General Meeting  
The optimized MCS solver is able to solve millions of load flow cases within a second, enabling the real-time Monte Carlo solution of the PLF.  ...  The application in this paper is to solve the probabilistic load flow (PLF) in real time, in order to cope with the uncertainties caused by the integration of renewable energy resources.  ...  At this step, we run the SIMD vector FBS solver in parallel in multiple threads on a multi-core CPU.  ... 
doi:10.1109/pesgm.2012.6344987 fatcat:lh26aqv76rgobhr54pwdo7izei
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