1,060 research outputs found
An interior-point and decomposition approach to multiple stage stochastic programming
There is no abstract of this report
A Generic Path Algorithm for Regularized Statistical Estimation
Regularization is widely used in statistics and machine learning to prevent
overfitting and gear solution towards prior information. In general, a
regularized estimation problem minimizes the sum of a loss function and a
penalty term. The penalty term is usually weighted by a tuning parameter and
encourages certain constraints on the parameters to be estimated. Particular
choices of constraints lead to the popular lasso, fused-lasso, and other
generalized penalized regression methods. Although there has been a lot
of research in this area, developing efficient optimization methods for many
nonseparable penalties remains a challenge. In this article we propose an exact
path solver based on ordinary differential equations (EPSODE) that works for
any convex loss function and can deal with generalized penalties as well
as more complicated regularization such as inequality constraints encountered
in shape-restricted regressions and nonparametric density estimation. In the
path following process, the solution path hits, exits, and slides along the
various constraints and vividly illustrates the tradeoffs between goodness of
fit and model parsimony. In practice, the EPSODE can be coupled with AIC, BIC,
or cross-validation to select an optimal tuning parameter. Our
applications to generalized regularized generalized linear models,
shape-restricted regressions, Gaussian graphical models, and nonparametric
density estimation showcase the potential of the EPSODE algorithm.Comment: 28 pages, 5 figure
An interior-point and decomposition approach to multiple stage stochastic programming
There is no abstract of this repor
Volume 2: Explicit, multistage upwind schemes for Euler and Navier-Stokes equations
The objective of this study was to develop a high-resolution-explicit-multi-block numerical algorithm, suitable for efficient computation of the three-dimensional, time-dependent Euler and Navier-Stokes equations. The resulting algorithm has employed a finite volume approach, using monotonic upstream schemes for conservation laws (MUSCL)-type differencing to obtain state variables at cell interface. Variable interpolations were written in the k-scheme formulation. Inviscid fluxes were calculated via Roe's flux-difference splitting, and van Leer's flux-vector splitting techniques, which are considered state of the art. The viscous terms were discretized using a second-order, central-difference operator. Two classes of explicit time integration has been investigated for solving the compressible inviscid/viscous flow problems--two-state predictor-corrector schemes, and multistage time-stepping schemes. The coefficients of the multistage time-stepping schemes have been modified successfully to achieve better performance with upwind differencing. A technique was developed to optimize the coefficients for good high-frequency damping at relatively high CFL numbers. Local time-stepping, implicit residual smoothing, and multigrid procedure were added to the explicit time stepping scheme to accelerate convergence to steady-state. The developed algorithm was implemented successfully in a multi-block code, which provides complete topological and geometric flexibility. The only requirement is C degree continuity of the grid across the block interface. The algorithm has been validated on a diverse set of three-dimensional test cases of increasing complexity. The cases studied were: (1) supersonic corner flow; (2) supersonic plume flow; (3) laminar and turbulent flow over a flat plate; (4) transonic flow over an ONERA M6 wing; and (5) unsteady flow of a compressible jet impinging on a ground plane (with and without cross flow). The emphasis of the test cases was validation of code, and assessment of performance, as well as demonstration of flexibility
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