Optimization-based models have been used to predict cellular behavior for over 25 years. The constraints in these models are derived from genome annotations, measured macromolecular composition of cells, and by measuring the cell's growth rate and metabolism in different conditions. The cellular goal (the optimization problem that the cell is trying to solve) can be challenging to derive experimentally for many organisms, including human or mammalian cells, which have complex metabolic capabilities and are not well understood. Existing approaches to learning goals from data include (a) estimating a linear objective function, or (b) estimating linear constraints that model complex biochemical reactions and constrain the cell's operation. The latter approach is important because often the known reactions are not enough to explain observations; therefore, there is a need to extend automatically the model complexity by learning new reactions. However, this leads to nonconvex optimization problems, and existing tools cannot scale to realistically large metabolic models. Hence, constraint estimation is still used sparingly despite its benefits for modeling cell metabolism, which is important for developing novel antimicrobials against pathogens, discovering cancer drug targets, and producing value-added chemicals. Here, we develop the first approach to estimating constraint reactions from data that can scale to realistically large metabolic models. Previous tools were used on problems having less than 75 reactions and 60 metabolites, which limits real-life-size applications. We perform extensive experiments using 75 large-scale metabolic network models for different organisms (including bacteria, yeasts, and mammals) and show that our algorithm can recover cellular constraint reactions. The recovered constraints enable accurate prediction of metabolic states in hundreds of growth environments not seen in training data, and we recover useful cellular goals even when some measurements are missing.

Most existing approaches to distributed sparse regression assume the data is partitioned by samples. However, for high-dimensional data (D >> N), it is more natural to partition the data by features. We propose an algorithm to distributed sparse regression when the data is partitioned by features rather than samples. Our approach allows the user to tailor our general method to various distributed computing platforms by trading-off the total amount of data (in bits) sent over the communication network and the number of rounds of communication. We show that an implementation of our approach is capable of solving L1-regularized L2 regression problems with millions of features in minutes.

BACKGROUND: Genome-scale models of metabolism and macromolecular expression (ME) significantly expand the scope and predictive capabilities of constraint-based modeling. ME models present considerable computational challenges: they are much (>30 times) larger than corresponding metabolic reconstructions (M models), are multiscale, and growth maximization is a nonlinear programming (NLP) problem, mainly due to macromolecule dilution constraints. RESULTS: Here, we address these computational challenges. We develop a fast and numerically reliable solution method for growth maximization in ME models using a quad-precision NLP solver (Quad MINOS). Our method was up to 45 % faster than binary search for six significant digits in growth rate. We also develop a fast, quad-precision flux variability analysis that is accelerated (up to 60× speedup) via solver warm-starts. Finally, we employ the tools developed to investigate growth-coupled succinate overproduction, accounting for proteome constraints. CONCLUSIONS: Just as genome-scale metabolic reconstructions have become an invaluable tool for computational and systems biologists, we anticipate that these fast and numerically reliable ME solution methods will accelerate the wide-spread adoption of ME models for researchers in these fields.

We describe algorithm MINRES-QLP and its FORTRAN 90 implementation for solving symmetric or Hermitian linear systems or least-squares problems. If the system is singular, MINRES-QLP computes the unique minimum-length solution (also known as the pseudoinverse solution), which generally eludes MINRES. In all cases, it overcomes a potential instability in the original MINRES algorithm. A positive-definite pre-conditioner may be supplied. Our FORTRAN 90 implementation illustrates a design pattern that allows users to make problem data known to the solver but hidden and secure from other program units. In particular, we circumvent the need for reverse communication. Example test programs input and solve real or complex problems specified in Matrix Market format. While we focus here on a FORTRAN 90 implementation, we also provide and maintain MATLAB versions of MINRES and MINRES-QLP.

BACKGROUND: Biological processes such as metabolism, signaling, and macromolecular synthesis can be modeled as large networks of biochemical reactions. Large and comprehensive networks, like integrated networks that represent metabolism and macromolecular synthesis, are inherently multiscale because reaction rates can vary over many orders of magnitude. They require special methods for accurate analysis because naive use of standard optimization systems can produce inaccurate or erroneously infeasible results. RESULTS: We describe techniques enabling off-the-shelf optimization software to compute accurate solutions to the poorly scaled optimization problems arising from flux balance analysis of multiscale biochemical reaction networks. We implement lifting techniques for flux balance analysis within the openCOBRA toolbox and demonstrate our techniques using the first integrated reconstruction of metabolism and macromolecular synthesis for E. coli. CONCLUSION: Our techniques enable accurate flux balance analysis of multiscale networks using off-the-shelf optimization software. Although we describe lifting techniques in the context of flux balance analysis, our methods can be used to handle a variety of optimization problems arising from analysis of multiscale network reconstructions.

We seek to solve convex optimization problems in composite form:

Image priors based on products have been recognized to offer many advantages because they allow simultaneous enforcement of multiple constraints. However, they are inconvenient for Bayesian inference because it is hard to find their normalization constant in closed form. In this paper, a new Bayesian algorithm is proposed for the image restoration problem that bypasses this difficulty. An image prior is defined by imposing Student-t densities on the outputs of local convolutional filters. A variational methodology, with a constrained expectation step, is used to infer the restored image. Numerical experiments are shown that compare this methodology to previous ones and demonstrate its advantages.

Probably more than any other group, authors Lustig, Marsten, and Shanno have led the way in demonstrating the effectiveness of interior methods for solving large, real-world linear programs. For several years they have written at length about things they have actually done. There are no pies in the sky, no secrets. They have explored a multitude of algorithmic ideas and implementation strategies, and they have done more than could be asked to share their experience with the rest of the world. Here, the authors look back on a decade's events that revived barrier methods for constrained optimization and eventually led to their production LP solver OB1. The results reported are indeed impressive. In this commentary, we focus mostly on the “engine”—the Cholesky factorizer—that has made OB1 such a practical success. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.

When describing active-set methods for linearly constrained optimization, it is often convenient to treat all constraints in a uniform manner.However, in many problems the linear constraints include simple bounds on the variables as well as general constraints.Special treatment of bound constraints in the implementation of a null-space active-set method yields significant advantages in computational effort and storage requirements.In this paper, we describe a particular implementation of the constraint-related steps of a null-space active-set method when the constraint matrix is dense and bounds are treated separately.These steps involve updates to the TQ factorization of the working set of constraints and the Cholesky factorization of the projected Hessian (or Hessian approximation).

An iterative method is given for solving Ax ~ffi b and minU Ax -b 112, where the matrix A is large and sparse.The method is based on the bidiagonalization procedure of Golub and Kahan.It is analytically equivalent to the standard method of conjugate gradients, but possesses more favorable numerical properties.Reliable stopping criteria are derived, along with estimates of standard errors for x and the condition number of A. These are used in the FORTRAN implementation of the method, subroutine LSQR.Numerical tests are described comparing I~QR with several other conjugate-gradient algorithms, indicating that I~QR is the most reliable algorithm when A is ill-conditioned.

article Free AccessArtifacts AvailableArtifacts Evaluated & Reusable Share on Algorithm 583: LSQR: Sparse Linear Equations and Least Squares Problems Authors: Christopher C. Paige School of Computer Science, McGill University, Montreal, Quebec, Canada H3A 2K6 School of Computer Science, McGill University, Montreal, Quebec, Canada H3A 2K6View Profile , Michael A. Saunders Department of Operations Research, Stanford University, Stanford, CA Department of Operations Research, Stanford University, Stanford, CAView Profile Authors Info & Claims ACM Transactions on Mathematical SoftwareVolume 8Issue 2June 1982 pp 195–209https://doi.org/10.1145/355993.356000Published:01 June 1982Publication History 548citation2,133DownloadsMetricsTotal Citations548Total Downloads2,133Last 12 Months125Last 6 weeks24 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my Alerts New Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF