A trust region method based on interior point techniques for nonlinear programming

By Richard H. Byrd, Jean Charles Gilbert, Jorge Nocedal. Mathematical programming, 2000

1,702 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/826385c6e255e8d8965dbddcde3a812397d8bab4

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In Computational Mechanics

In Computational Theory and Mathematics

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Citations in the corpus

Variations and extension of the convex–concave procedure (2016, background): “Many approximation procedures, like SQP, require trust regions which limit progress at an iteration to a region where the approximation is valid (Byrd et al. 2000).”
Handbook of Semidefinite Programming (2000, background): “In recent years, a number of approaches were proposed to generalize interior-point methods to nonconvex programs, see for example Argaez and Tapia [46], Byrd, Gilbert, and Nocedal [157], Coleman and Li [172], Conn, Gould, and Toint [174], Forsgren and Gill [260], Gay, Overton, and Wright [284], Sarg”
Time-domain fitting of battery electrochemical impedance models (2015, methodology): “The default interior point optimisation algorithm [44] was chosen.”
On Probabilistic Shaping of Quadrature Amplitude Modulation for the Nonlinear Fiber Channel (2016, methodology): “This optimization is conducted in MATLAB using the interior point algorithm [44].”
Knitro: An Integrated Package for Nonlinear Optimization (2006, methodology): “In the interior point algorithms, our heuristics are based on the theory developed in [3].”
SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization (2002, background): “LOQO [78] and KNITRO [17, 16] are examples of large-scale optimization packages that treat inequality constraints by a primal-dual interior method.”
An interior algorithm for nonlinear optimization that combines line search and trust region steps (2006, methodology): “The resulting algorithm possesses global convergence properties similar to those of the algorithms implemented in FilterSQP [15] and Knitro [5].”
A Computationally Efficient Feasible Sequential Quadratic Programming Algorithm (2000, background): “There has been a great deal of interest recently in interior point algorithms for nonconvex nonlinear programming (see, e.g., [5, 6, 26, 4 , 18, 25]).”
Optimization and uncertainty analysis of ODE models using 2nd order adjoint sensitivity analysis (2018, methodology): “…such as the Gauss-Newton-type methods combined with trust-region algorithms (Coleman & Li, 1996; Dennis et al., 1981), or constraint optimization algorithms, which compute descent direction with (quasi-)Newton-type methods combined with interior-point or trust-region algorithms (Byrd et al., 2000).”
CUTEr and SifDec: A constrained and unconstrained testing environment, revisited (2003, methodology): “The KNITRO software [ 5 ] is maintained by Jorge Nocedal (nocedal@ece.northwestern.edu) and Richard Waltz (rwaltz@ece.northwestern.edu).”
The interior-point revolution in optimization: History, recent developments, and lasting consequences (2004, methodology): “3), primal-dual methods based on properties of xμ are increasingly popular for solving general nonlinear programming problems; see, for example, the recent papers [8, 4, 11, 7, 14].”
Interior Methods for Nonlinear Optimization (2002, methodology): “Because of inherent flaws in the classical primal barrier method, primal-dual methods based on properties of x(μ) are increasingly popular for solving general nonlinear programming problems; see, for example, the recent papers [14, 24, 31, 39, 46, 93, 97, 103].”
Trajectory Planning for Quadrotor Swarms (2018, background): “Iterative refinement is similar in spirit to sequential quadratic programming [33] and sequential convex programming [34].”
Entropy Search for Information-Efficient Global Optimization (2011, methodology): “…to a number of numerical optimization algorithms: Trust-Region-Reﬂective (Coleman and Li, 1996, 1994), Active-Set (Powell, 1978b,a), interior point (Byrd et al., 1999, 2000; Waltz et al., 2006), and a na¨ıvely projected version of the BFGS algorithm (Broyden et al., 1965; Fletcher, 1970;…”