UOBYQA: unconstrained optimization by quadratic approximation

By M. Powell. Mathematical programming, 2002

408 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/8838f250693a9e06345da68926f27ccdab4f1d02

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In Computational Theory and Mathematics

In Numerical Analysis

Citations in the corpus

Retrieval of the full magnetic vector with the He I multiplet at 1083 nm. Maps of an emerging flux region (2004, methodology): “…robustness we compared the results of the genetic algorithm with the ones obtained with UOBYQA (Unconstrained Optimization BY Quadratic Approximation, Powell 2002), a code which estimates the first and second derivatives of the parameters in the fitness function using quadratic approximations.”
APOGEE Data and Spectral Analysis from SDSS Data Release 16: Seven Years of Observations Including First Results from APOGEE-South (2020, methodology): “…minimizing algorithm in FERRE from the default Nelder–Mead algorithm (Nelder & Mead 1965), identified in the code with the option ALGOR=1, to the Unconstrained Optimization BY Quadratic Approximation (UOBYQA; Powell 2002), ALGOR= 3 in FERRE, and this led to a compensating increase in analysis time.”
Derivative-free optimization: a review of algorithms and comparison of software implementations (2012, neutral): “Powell [112] and Conn et al.”
A View of Algorithms for Optimization without Derivatives 1 (2007, methodology): “I have assembled these ingredients and more into the UOBYQA Fortran software (Powell, 2002), where UOBYQA denotes Unconstrained Optimization BY Quadratic Approximation.”
Recent advances in trust region algorithms (2015, methodology): “Methods using (6.2) are given by Winﬁeld [137,138] and Powell [96].”
Constrained Global Optimization of Expensive Black Box Functions Using Radial Basis Functions (2005, methodology): “Another class of methods are the derivative-free optimization methods by Powell (1994, 2000, 2002) and by Conn et al. (1997) which utilize multivariate polynomial interpolation models within a trust-region framework.”
The NEWUOA software for unconstrained optimization without derivatives (2006, methodology): “…NEWUOA is given in Section 2, but m (the number of interpolation conditions) and the way of updating Q are not mentioned, so most of the outline applies also to the UOBYQA software of the author (Powell, 2002), where each quadratic model is defined by interpolation to 1 2 (n+1)(n+2) values of F .”
Reinforcement Learning in Continuous State and Action Spaces (2012, background): “Another approach is to construct an easier solvable (e.g., quadratic)model of the function that is to be optimized and then maximize this model analytically(see, e.g., Powell, 2002, 2006; Huyer and Neumaier, 2008).”
A Stochastic Radial Basis Function Method for the Global Optimization of Expensive Functions (2007, methodology): “For the derivative-free trust region method, we used UOBYQA (Powell 2002), which is implemented in Matlab by Vanden Berghen and Bersini (2005).”
Aggregation Functions: A Guide for Practitioners (2007, methodology): “It is a nonsmooth but convex optimization problem, and there are efficient numerical methods for its solution [9, 139, 154, 205].”
Benchmarking Derivative-Free Optimization Algorithms (2009, background): “Since the limiting value of ρ s can be interpreted as the reliability of the solver, we see that (2.10) shows that the data proﬁle d s measures the reliability of the solver (for a given tolerance τ ) as a function of the budget µ f .”