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Efficient Computation of Sparse Hessians using Coloring and Automatic Differentiation
"... The computation of a sparse Hessian matrix H using automatic dierentiation (AD) can be made ecient using the following fourstep procedure. 1. Determine the sparsity structure of H. 2. Obtain a seed matrix S that denes a column partition of H using a specialized coloring on the adjacency graph of H. ..."
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Cited by 16 (6 self)
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The computation of a sparse Hessian matrix H using automatic dierentiation (AD) can be made ecient using the following fourstep procedure. 1. Determine the sparsity structure of H. 2. Obtain a seed matrix S that denes a column partition of H using a specialized coloring on the adjacency graph of H. 3. Compute the compressed Hessian matrix B = HS. 4. Recover the numerical values of the entries of H from B. The coloring variant used in the second step depends on whether the recovery in the fourth step is direct or indirect: a direct method uses star coloring, and an indirect method uses acyclic coloring. In an earlier work, we had designed and implemented eective heuristic algorithms for these two NPhard coloring problems. Recently, we integrated part of the developed software with the AD tool ADOLC, which has recently acquired a sparsity detection capability. In this paper, we provide a detailed description and analysis of the recovery algorithms, and experimentally demonstrate the ecacy of the coloring techniques in the overall process of computing the Hessian of a given function using ADOLC as an example
Stackelberg games for adversarial prediction problems
 In Proceedings of the 17th ACM SIGKDD international conference on Knowledge discovery and data mining
, 2011
"... The standard assumption of identically distributed training and test data is violated when test data are generated in response to a predictive model. This becomes apparent, for example, in the context of email spam filtering, where an email service provider employs a spam filter and the spam sender ..."
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Cited by 15 (1 self)
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The standard assumption of identically distributed training and test data is violated when test data are generated in response to a predictive model. This becomes apparent, for example, in the context of email spam filtering, where an email service provider employs a spam filter and the spam sender can take this filter into account when generating new emails. We model the interaction between learner and data generator as a Stackelberg competition in which the learner plays the role of the leader and the data generator may react on the leader’s move. We derive an optimization problem to determine the solution of this game and present several instances of the Stackelberg prediction game. We show that the Stackelberg prediction game generalizes existing prediction models. Finally, we explore properties of the discussed models empirically in the context of email spam filtering.
Improving ultimate convergence of an Augmented Lagrangian method
, 2007
"... Optimization methods that employ the classical PowellHestenesRockafellar Augmented Lagrangian are useful tools for solving Nonlinear Programming problems. Their reputation decreased in the last ten years due to the comparative success of InteriorPoint Newtonian algorithms, which are asymptoticall ..."
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Cited by 14 (0 self)
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Optimization methods that employ the classical PowellHestenesRockafellar Augmented Lagrangian are useful tools for solving Nonlinear Programming problems. Their reputation decreased in the last ten years due to the comparative success of InteriorPoint Newtonian algorithms, which are asymptotically faster. In the present research a combination of both approaches is evaluated. The idea is to produce a competitive method, being more robust and efficient than its “pure” counterparts for critical problems. Moreover, an additional hybrid algorithm is defined, in which the Interior Point method is replaced by the Newtonian resolution of a KKT system identified by the Augmented Lagrangian algorithm. The software used in this work is freely available through the Tango Project web page:
Nonlinear programming strategies for state estimation and model predictive control
 In Nonlinear Model Predictive Control
, 2009
"... Abstract. Sensitivitybased strategies for online moving horizon estimation (MHE) and nonlinear model predictive control (NMPC) are presented both from a stability and computational perspective. These strategies make use of fullspace interiorpoint nonlinear programming (NLP) algorithms and NLP se ..."
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Cited by 13 (8 self)
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Abstract. Sensitivitybased strategies for online moving horizon estimation (MHE) and nonlinear model predictive control (NMPC) are presented both from a stability and computational perspective. These strategies make use of fullspace interiorpoint nonlinear programming (NLP) algorithms and NLP sensitivity concepts. In particular, NLP sensitivity allows us to partition the solution of the optimization problems into background and negligible online computations, thus avoiding the problem of computational delay even with large dynamic models. We demonstrate these developments through a distributed polymerization reactor model containing around 10,000 differential and algebraic equations (DAEs).
ON MUTUAL IMPACT OF NUMERICAL LINEAR ALGEBRA AND LARGESCALE OPTIMIZATION WITH FOCUS ON INTERIOR POINT METHODS
, 2008
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Singular arcs in the generalized Goddard’s Problem
, 2007
"... We investigate variants of Goddard’s problems for nonvertical trajectories. The control is the thrust force, and the objective is to maximize a certain final cost, typically, the final mass. In this article, performing an analysis based on the Pontryagin Maximum Principle, we prove that optimal traj ..."
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Cited by 12 (6 self)
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We investigate variants of Goddard’s problems for nonvertical trajectories. The control is the thrust force, and the objective is to maximize a certain final cost, typically, the final mass. In this article, performing an analysis based on the Pontryagin Maximum Principle, we prove that optimal trajectories may involve singular arcs (along which the norm of the thrust is neither zero nor maximal), that are computed and characterized. Numerical simulations are carried out, both with direct and indirect methods, demonstrating the relevance of taking into account singular arcs in the control strategy. The indirect method we use is based on our previous theoretical analysis and consists in combining a shooting method with an homotopic method. The homotopic approach leads to a quadratic regularization of the problem and is a way to tackle with the problem of nonsmoothness of the optimal control.
nconsistent parameter estimation for systems of ordinary differential equations: bypassing numerical integration via smoothing. Bernoulli 18 (3), 1061–1098 (2012). Shota Gugushvili and Peter Spreij
 of Lecture Notes in Statistics
, 1989
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Dynamic updates of the barrier parameter in primaldual methods for nonlinear programming
, 2006
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Numerical study of optimal trajectories with singular arcs for space launcher problems
 in "AIAA J. of Guidance, Control and Dynamics", To appear, 2009. International PeerReviewed Conference/Proceedings
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