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Matrix Scaling and Balancing via Box Constrained Newton's Method and Interior Point Methods
[article]
2017
arXiv
pre-print
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We complement our results by providing a separate algorithm that uses an interior-point method and runs in time O(m^3/2 (1/ϵ)). ...
We then show that in the context of the specific functions capturing matrix scaling and balancing, we can leverage and generalize the work on Laplacian system solving to make the algorithms obtained via ...
This iterative procedure can be viewed as a "box-constrained" variant of the Newton's method. ...
arXiv:1704.02310v2
fatcat:dcsy6vs65zgizoil5yp43mqfiy
Book announcements
1990
Discrete Applied Mathematics
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Quasi-Newton
methods (Hessian matrix updates. The DFP and BFGS
formulas).
Finite differences and scaling (Finite differences.
Scaling). Active set strategies (Adding and
deleting constraints. ...
Nature
of stationary
points).
Convexity
(Convex
sets and functions.
Differentiable
functions).
Local exploration
(Gradient
descent. Newton's method). ...
doi:10.1016/0166-218x(90)90013-3
fatcat:5jdut3iylrffvcnyiogm2tfe24
Parallel nonlinear predictive control
2012
2012 50th Annual Allerton Conference on Communication, Control, and Computing (Allerton)
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We present a numerical study examining the capabilities of state-of-the-art interior point optimization solvers to utilize parallel linear algebra. ...
We focus on the ability of these methods to handle, in a systematic way, large-scale systems with nonlinearities and constraints. ...
Watson Research Center for solving an installation issue with WSMP, and the Ipopt authors for all of their development efforts. ...
doi:10.1109/allerton.2012.6483201
dblp:conf/allerton/KelmanB12
fatcat:mj3ygl6lwvhufh6i7llumnfomq
Least squares problems with inequality constraints as quadratic constraints
2010
Linear Algebra and its Applications
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Results are compared with solutions found by lsqlin, and the quadratically constrained formulation is solved using the L-curve, maximum a posteriori estimation (MAP), and the χ 2 regularization method. ...
The χ 2 regularization method with quadratic constraints is the most effective method for solving least squares problems with box constraints. Linear least squares, Box constraints, Regularization ...
Interior point methods use variants of Newton's method to solve the KKT equality conditions for (1) . ...
doi:10.1016/j.laa.2009.04.017
fatcat:bhwy5mtiubggtncia3tku5v5ru
Numerical methods for large-scale nonlinear optimization
2005
Acta Numerica
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State-of-the-art algorithms for solving unconstrained, bound-constrained, linearly-constrained and nonlinearly-constrained problems are discussed. ...
Recent developments in numerical methods for solving large differentiable nonlinear optimization problems are reviewed. ...
Numerical methods for large-scale nonlinear optimization ...
doi:10.1017/s0962492904000248
fatcat:dz3twiovzfekxawl2h3wfi3m44
A computational framework for simulation of biogeochemical tracers in the ocean
2007
Global Biogeochemical Cycles
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This paper describes the key features and advantages of the transport matrix method, and illustrates its application to a series of realistic problems in chemical and biological oceanography. ...
the task of simulating tracers to a sequence of simple matrix-vector products. ...
I am grateful to Stephanie Dutkiewicz and Mick Follows for sharing their expertise of the MIT biogeochemical model, and Patrick Heimbach for computing the ECCO matrix. ...
doi:10.1029/2007gb002923
fatcat:d6eqk74dtjfaxfkzsfxt2r7mfu
Augmented Lagrangian and Proximal Methods for Constrained Structured Optimization
2021
Zenodo
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This is based on the proposed proximal augmented Lagrangian framework and weaves together the proximal point algorithm and a damped semismooth Newton's method. ...
The inner subproblems can be solved by any method for structured optimization and the overall algorithm can be made matrix-free. ...
Birgin and J. M. Martínez. "Large-scale active-set box-constrained optimization method with spectral projected gradients". In: Computational Optimization and Applications . ( ), pp. -. [ ] E. D. ...
doi:10.5281/zenodo.4972536
fatcat:2et67kr2b5bpfpnp5vodnr7eci
Optimal Experimental Design for Constrained Inverse Problems
[article]
2017
arXiv
pre-print
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To overcome the lack of non-differentiability in active set methods for inequality constraints problems, we use a relaxed interior point method. ...
importance of OED for constrained problems. ...
Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. ...
arXiv:1708.04740v1
fatcat:s7dtzjlg3jdhzp6hvlk65qstzu
Spectral Gradient Methods for Linearly Constrained Optimization
2005
Journal of Optimization Theory and Applications
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Each outer iteration involves the application of the previously defined preconditioned spectral gradient method for linear equality constrained problems. ...
The associated extended KKT matrix remains constant unless the process is reinitiated. In ordinary inner iterations, only the right hand side of the KKT system changes. ...
They have been applied to find local minimizers of large scale problems [4, 5, 22] , and also to explore faces of large dimensions in box-constrained optimization (see [3] and [12] ). ...
doi:10.1007/s10957-005-2093-3
fatcat:cg4vefgymvewtp2l3usuczbglu
Faster and more accurate computation of the H_∞ norm via optimization
[article]
2019
arXiv
pre-print
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Unlike the standard algorithm, our modified approach can also calculate the H_∞ norm to full precision with little extra work, and also offers more opportunity to further accelerate its performance via ...
In this paper, we propose an improved method for computing the H_∞ norm of linear dynamical systems that results in a code that is often several times faster than existing methods. ...
iterations and particularly when using the Newton's method variants. ...
arXiv:1707.02497v6
fatcat:q27l6n2zvrdwfbw2svxe7bqqni
Fast Parallel Algorithms for Short-Range Molecular Dynamics
1995
Journal of Computational Physics
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, and Cray T3D. ...
Trade-offs between the three algorithms and guidelines for adapting them to more complex molecular dynamics simulations are also discussed. ...
They include particle-mesh algorithms [31] which scale as f (M )N where M is the number of mesh points, hierarchical methods [6] which scale as N log(N ), and fast-multipole methods [23] which scale ...
doi:10.1006/jcph.1995.1039
fatcat:2xmytcwf3ncifdw4lak3jaj6bq
Mathematical programs with complementarity constraints in traffic and telecommunications networks
2008
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
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has paved the way for finding local solutions of MPCCs via standard NLP techniques. ...
An example is toll design in traffic networks, which attempts to reduce total travel time by choosing which arcs to toll and what toll levels to impose. ...
The author gratefully acknowledges the input of Frank Kelly, Gaurav Raina, Mike Smith and Agachai Sumalee on the literature of network equilibria, and Michael Ferris, Jong-Shi Pang and Stefan Scholtes ...
doi:10.1098/rsta.2008.0026
pmid:18325868
fatcat:uphboppnineahftr7hvttac6iq
Two numerical methods for optimizing matrix stability
2002
Linear Algebra and its Applications
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The spectral abscissa α(X) is a continuous but non-smooth, in fact non-Lipschitz, function of the matrix argument X, and finding a global minimizer of α(A(x)) is hard. ...
Burke et al. / Linear Algebra and its Applications 351-352 (2002) approaching α(X) as δ → 0 and the largest eigenvalue of 1 2 (X + X T ) as δ → 1. ...
The approach fell out of favor in the 1970s but was revived in the 1980s and 1990s [32] , following the explosion of interest in interior point methods for linear and convex programming. ...
doi:10.1016/s0024-3795(02)00260-4
fatcat:kor665cn3vbr5dhdmn5pcwaaoe
Differentiable Collision Avoidance Using Collision Primitives
[article]
2022
arXiv
pre-print
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Optimization-based motion planning is one method, that often heavily relies on distance computations between robots and obstacles. ...
To improve performance, many different methods suggested to use collision primitives, i.e. simple shapes that approximate the more complex rigid bodies, and that are simpler to compute distances to and ...
Our method produced smoother velocities and found a more direct path. method and use it as a starting point for the optimization. ...
arXiv:2204.09352v1
fatcat:fhfrnxzwyngl7gmhm6exlsltxm
A Scaled Gradient Projection Method for Bayesian Learning in Dynamical Systems
2015
SIAM Journal on Scientific Computing
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In particular, we propose both a generalization of the split gradient approach to design the scaling matrix in the presence of box constraints, and an effective implementation of the gradient and objective ...
In this paper we address this problem by means of a scaled gradient projection algorithm, in which the scaling matrix and the steplength parameter play a crucial role to provide a meaning solution in a ...
To motivate the introduction of the scaling matrix, one can think, for example, of the Newton's method, which actually scales the gradient direction with the inverse Hessian, while other practical choices ...
doi:10.1137/140973529
fatcat:gliuual2mnfalgx34b3qzfrpia
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