Remark on “algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound constrained optimization”

Morales, José Luís; Nocedal, Jorge

doi:10.1145/2049662.2049669

Cited by 369 publications

(224 citation statements)

References 5 publications

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“…In cases where the analyst wishes to impose prior constraints on the parameter space, the objective function may be maximized using constrained non-linear optimization methods, such as the L-BFGS-B algorithm (Byrd et al, 1995;Zhu et al, 1997;and Morales and Nocedal, 2011). For example, when estimating travel mode choice models, taste coefficients denoting sensitivities to travel times and costs are frequently constrained to be non-positive.…”

Section: An Expectation Maximization (Em) Algorithm For Model Estimationmentioning

confidence: 99%

Random taste heterogeneity in discrete choice models: Flexible nonparametric finite mixture distributions

Vij

Krueger

2017

Transportation Research Part B: Methodological

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This study proposes a mixed logit model with multivariate nonparametric finite mixture distributions. The support of the distribution is specified as a high-dimensional grid over the coefficient space, with equal or unequal intervals between successive points along the same dimension; the location of each point on the grid and the probability mass at that point are model parameters that need to be estimated. The framework does not require the analyst to specify the shape of the distribution prior to model estimation, but can approximate any multivariate probability distribution function to any arbitrary degree of accuracy. The grid with unequal intervals, in particular, offers greater flexibility than existing multivariate nonparametric specifications, while requiring the estimation of a small number of additional parameters. An expectation maximization algorithm is developed for the estimation of these models. Multiple synthetic datasets and a case study on travel mode choice behavior are used to demonstrate the value of the model framework and estimation algorithm. Compared to extant models that incorporate random taste heterogeneity through continuous mixture distributions, the proposed model provides better out-of-sample predictive ability. Findings reveal significant differences in willingness to pay measures between the proposed model and extant specifications. The case study further demonstrates the ability of the proposed model to endogenously recover patterns of attribute non-attendance and choice set formation.3

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Section: An Expectation Maximization (Em) Algorithm For Model Estimationmentioning

confidence: 99%

Random taste heterogeneity in discrete choice models: Flexible nonparametric finite mixture distributions

Vij

Krueger

2017

Transportation Research Part B: Methodological

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“…With M being a hyperrectangle of R dM , we use L-BFGS-B (Limited-memory Broyden-Fletcher-Goldfarb-Shanno Bound constrained (Byrd et al, 1995;Zhu et al, 1997), version 3.0 (Morales and Nocedal, 2011)), a quasi-Newton method for bound-constrained optimization, to minimize the error. L-BFGS-B use an approximation of the Hessian matrix to direct the optimization (because the Hessian cannot be directly computed, it is approximated using finite differences).…”

Section: Inverse Modelmentioning

confidence: 99%

Behavioral Diversity Generation in Autonomous Exploration through Reuse of Past Experience

Benureau

Oudeyer

2016

Front. Robot. AI

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The production of behavioral diversity -producing a diversity of effects -is an essential strategy for robots exploring the world when facing situations where interaction possibilities are unknown or non-obvious. It allows to discover new aspects of the environment that cannot be inferred or deduced from available knowledge. However, creating behavioral diversity in situations where it is most crucial -new and unknown ones -is far from trivial. In particular in large and redundant sensorimotor spaces, only small areas are interesting to explore for any practical purpose. When the environment does not provide clues or gradient toward those areas, trying to discover those areas relies on chance. To address this problem, we introduce a method to create behavioral diversity in a new sensorimotor task by re-enacting actions that allowed to produce behavioral diversity in a previous task, along with a measure that quantifies this diversity. We show that our method can learn how to interact with an object by reusing experience from another, that it adapts to instances of morphological changes and of dissimilarity between tasks, and how scaffolding behaviors can emerge by simply switching the attention of the robot to different parts of the environment. Finally, we show that the method can robustly use simulated experiences and crude cognitive models to generate behavioral diversity in real robots.

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“…Among all possible algorithms and software, quasi-Newton methods are known to be efficient [5,22]. In our numerical experiments, we use the FORTRAN code L-BFGS-B [8,30] which has been recently upgraded to version 3.0 [21]. We use the default parameters of the code.…”

Section: Computing the Boundsmentioning

confidence: 99%

Improved semidefinite bounding procedure for solving Max-Cut problems to optimality

2012

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To cite this version:Nathan Krislock, Jérôme Malick, Frédéric Roupin. Improved semidefinite bounding procedure for solving Max-Cut problems to optimality. Mathematical Programming, Springer Verlag, 2014, 143 (1-2), pp.61-86. <10.1007/s10107-012-0594-z>. Improved semidefinite bounding procedure for solving Max-Cut problems to optimality AbstractWe present an improved algorithm for finding exact solutions to Max-Cut and the related binary quadratic programming problem, both classic problems of combinatorial optimization. The algorithm uses a branch-(and-cut-)and-bound paradigm, using standard valid inequalities and nonstandard semidefinite bounds. More specifically, we add a quadratic regularization term to the strengthened semidefinite relaxation in order to use a quasi-Newton method to compute the bounds. The ratio of the tightness of the bounds to the time required to compute them can be controlled by two real parameters; we show how adjusting these parameters and the set of strengthening inequalities gives us a very efficient bounding procedure. Embedding our bounding procedure in a generic branch-and-bound platform, we get a competitive algorithm: extensive experiments show that our algorithm dominates the best existing method.

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Remark on “algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound constrained optimization”

Cited by 369 publications

References 5 publications

Random taste heterogeneity in discrete choice models: Flexible nonparametric finite mixture distributions

Random taste heterogeneity in discrete choice models: Flexible nonparametric finite mixture distributions

Behavioral Diversity Generation in Autonomous Exploration through Reuse of Past Experience

Improved semidefinite bounding procedure for solving Max-Cut problems to optimality

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