Derivative-Free and Blackbox Optimization

Audet, Charles; Hare, Warren

doi:10.1007/978-3-319-68913-5

Cited by 382 publications

(327 citation statements)

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“…Since both models are non-linear, it is essential to implement a routine that effectively explores the parameter space to converge to a global minimum. We, therefore, adopt a variant of the direct search method, which is a derivative-free optimisation strategy that is becoming quite indispensable in practice (Audet & Hare 2017). The mesh adaptive direct search (MADS) is one such method that generates meshes of the parameter space (Audet & Dennis, Jr. 2006).…”

Section: Optimisation Algorithmmentioning

confidence: 99%

Nuclear kinematics in nearby AGN – I. An ALMA perspective on the morphology and kinematics of the molecular CO(2–1) emission

Nagar

Finlez

Storchi‐Bergmann

et al. 2019

Monthly Notices of the Royal Astronomical Society

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We present the molecular gas morphology and kinematics of seven nearby Seyfert galaxies obtained from our 230 GHz ALMA observations. The CO J=2-1 kinematics within the inner ∼ 30 ( 9 kpc) reveals rotation patterns that have been explored using the Bertola rotation model and a modified version of the Kinemetry package. The latter algorithm reveals various deviations from pure circular rotation in the inner kiloparsec of all seven galaxies, including kinematic twists, decoupled and counter-rotating cores. A comparison of the global molecular gas and stellar kinematics show overall agreement in the position angle of the major axis and the systemic velocity, but larger discrepancies in the disc inclination. The residual maps obtained with both the methods shows the presence of non-circular motions in most of the galaxies. Despite its importance, a detailed interpretation of the physics responsible for noncircular motions will be discussed in a forthcoming work.

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Section: Optimisation Algorithmmentioning

confidence: 99%

Nuclear kinematics in nearby AGN – I. An ALMA perspective on the morphology and kinematics of the molecular CO(2–1) emission

Nagar

Finlez

Storchi‐Bergmann

et al. 2019

Monthly Notices of the Royal Astronomical Society

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“…Most other DFO methods for nonsmooth optimization fall under the catergory of direct search methods [9,Part 3]. Direct search methods work by setting an incumbent solution and then polling around the incumbent solution to seek a point that provides a better function value.…”

Section: Theoretical Comparison To Other Dfo Methodsmentioning

confidence: 99%

“…DFO algorithms can be split broadly into two categories, direct search methods and model-based methods. Model-based methods approximate the objective function with a model function, and then use the model to guide the optimization algorithm [9,Part 4].…”

Section: Introductionmentioning

confidence: 99%

A derivative-free 𝒱𝒰-algorithm for convex finite-max problems

Hare

Planiden

Sagastizábal

2019

Optimization Methods and Software

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The VU-algorithm is a superlinearly convergent method for minimizing nonsmooth, convex functions. At each iteration, the algorithm works with a certain V-space and its orthogonal U -space, such that the nonsmoothness of the objective function is concentrated on its projection onto the V-space, and on the U -space the projection is smooth. This structure allows for an alternation between a Newtonlike step where the function is smooth, and a proximal-point step that is used to find iterates with promising VU-decompositions. We establish a derivative-free variant of the VU-algorithm for convex finite-max objective functions. We show global convergence and provide numerical results from a proof-of-concept implementation, which demonstrates the feasibility and practical value of the approach. We also carry out some tests using nonconvex functions and discuss the results.

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“…Most existing methods fix the tangents and only optimize curves. After identifying the tangents, we fix them and use the NOMAD optimization software (Audet and Dennis, 2006;Audet and Hare, 2017;Abramson et al, 2018;Li et al, 2016) to optimize the circular curves and transition curves.…”

Section: Fix Tangents and Only Optimize Curvesmentioning

confidence: 99%

A Method for Automatically Recreating the Horizontal Alignment Geometry of Existing Railways

Schonfeld

et al. 2018

Computer aided Civil Eng

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Periodic recreation of existing railway horizontal alignment geometry is needed for smoothing the deviations arising from train operations. It is important for calibrating track and rebuilding existing railways to ensure safety and comfort. Track calibration repairs the existing distorted track centerline to match the smoothed recreated alignment, which may differ considerably from the originally designed track centerline. Identifying the boundaries of all the geometric elements including tangents, circular curves, and transition curves is the key problem. Existing methods recreate the horizontal alignment semi‐automatically and can only generate a locally optimized solution while considering a few constraints. Based on the principle that the attributions of all the measured points to geometric elements should be consistent with the ranges of recreated geometric elements (i.e., for points‐alignment consistency), a method called swing iterations is proposed to reclassify point placements and identify all the tangents, circular curves, and transition curves simultaneously. In a swing iteration, the boundary of a geometric element segment repeatedly changes from left to right, then from the right to left, and finally stabilizes. Before the swing iterations, preliminary tangents and curves are identified based on the heading gradient (i.e., the rate of change of heading), and are set as initial values for the swing iterations. A genetic algorithm is developed to further refine the entire recreated alignment after the swing iterations. In the above processes, multiple constraints are handled. Applications demonstrate that this method can identify all horizontal geometric elements automatically and generate an optimized recreated alignment geometry for an existing railway while satisfying all the applicable constraints.

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Derivative-Free and Blackbox Optimization

Cited by 382 publications

References 0 publications

Nuclear kinematics in nearby AGN – I. An ALMA perspective on the morphology and kinematics of the molecular CO(2–1) emission

Nuclear kinematics in nearby AGN – I. An ALMA perspective on the morphology and kinematics of the molecular CO(2–1) emission

A derivative-free 𝒱𝒰-algorithm for convex finite-max problems

A Method for Automatically Recreating the Horizontal Alignment Geometry of Existing Railways

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