6,158 research outputs found
Limited-memory BFGS Systems with Diagonal Updates
In this paper, we investigate a formula to solve systems of the form (B +
{\sigma}I)x = y, where B is a limited-memory BFGS quasi-Newton matrix and
{\sigma} is a positive constant. These types of systems arise naturally in
large-scale optimization such as trust-region methods as well as
doubly-augmented Lagrangian methods. We show that provided a simple condition
holds on B_0 and \sigma, the system (B + \sigma I)x = y can be solved via a
recursion formula that requies only vector inner products. This formula has
complexity M^2n, where M is the number of L-BFGS updates and n >> M is the
dimension of x
An Alternating Trust Region Algorithm for Distributed Linearly Constrained Nonlinear Programs, Application to the AC Optimal Power Flow
A novel trust region method for solving linearly constrained nonlinear
programs is presented. The proposed technique is amenable to a distributed
implementation, as its salient ingredient is an alternating projected gradient
sweep in place of the Cauchy point computation. It is proven that the algorithm
yields a sequence that globally converges to a critical point. As a result of
some changes to the standard trust region method, namely a proximal
regularisation of the trust region subproblem, it is shown that the local
convergence rate is linear with an arbitrarily small ratio. Thus, convergence
is locally almost superlinear, under standard regularity assumptions. The
proposed method is successfully applied to compute local solutions to
alternating current optimal power flow problems in transmission and
distribution networks. Moreover, the new mechanism for computing a Cauchy point
compares favourably against the standard projected search as for its activity
detection properties
OPTIMASS: A Package for the Minimization of Kinematic Mass Functions with Constraints
Reconstructed mass variables, such as , , , and
, play an essential role in searches for new physics at hadron
colliders. The calculation of these variables generally involves constrained
minimization in a large parameter space, which is numerically challenging. We
provide a C++ code, OPTIMASS, which interfaces with the MINUIT library to
perform this constrained minimization using the Augmented Lagrangian Method.
The code can be applied to arbitrarily general event topologies and thus allows
the user to significantly extend the existing set of kinematic variables. We
describe this code and its physics motivation, and demonstrate its use in the
analysis of the fully leptonic decay of pair-produced top quarks using the
variables.Comment: 39 pages, 12 figures, (1) minor revision in section 3, (2) figure
added in section 4.3, (3) reference added and (4) matched with published
versio
A quasi-Newton proximal splitting method
A new result in convex analysis on the calculation of proximity operators in
certain scaled norms is derived. We describe efficient implementations of the
proximity calculation for a useful class of functions; the implementations
exploit the piece-wise linear nature of the dual problem. The second part of
the paper applies the previous result to acceleration of convex minimization
problems, and leads to an elegant quasi-Newton method. The optimization method
compares favorably against state-of-the-art alternatives. The algorithm has
extensive applications including signal processing, sparse recovery and machine
learning and classification
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