Interior Methods for Nonlinear Optimization

By Anders Forsgren, Philip E. Gill, Margaret H. Wright. SIAM Review, 2002

770 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/396a567f86725c166edbf43024f39d52d1504f29

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Citations in the corpus

On Augmented Lagrangian Methods with General Lower-Level Constraints (2007, methodology): “Most practical nonlinear programming methods published after 2001 rely on (a combination of) sequential quadratic programming (SQP), Newton-like, or barrier approaches [1, 5, 14, 16, 18, 19, 26, 27, 28, 29, 35, 38, 44, 45, 46, 48, 49, 50].”
Reduced-basis techniques for rapid reliable optimization of systems described by affinely parametrized coercive elliptic partial differential equations (2007, background): “…the computational cost (Alexandrov and Dennis 1995; Dennis and Torczon 1997; Patera et al. 2000; Ravindran 1998) and, relatedly, increasing the fidelity and reliability of optimization procedures (Byrd et al. 1999; Forsgren et al. 2002; Forsgren and Gill 1998; Gill et al. 2002; Gould 2003).”
Numerical lower bound shakedown analysis of engineering structures (2011, methodology): “Among the different approaches for the solution of nonlinear optimization problems, we choose the widely used interior-point method [8–11], which has been implemented into several software packages for general nonlinear programming, such as LOQO [12,13], KNITRO [14,15] and IPOPT [16,17].”
Sequential integer programming methods for stress constrained topology optimization (2007, neutral): “Forsgren et al. (2002) or Nocedal and Wright (2006).”
Numerical Maximisation of Likelihood: A Neglected Alternative to EM? (2014, background): “By the 1980s, the received wisdom was that they suffered from ill-conditioning that rendered them unreliable, but they have turned out to be the main weapon in the hands of the revolutionaries in the ‘interior-point revolution’ of constrained optimisation (Forsgren et al., 2002; Wright, 2004).”
On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming (2006, background): “Over the past 15 years, there has also been a better understanding of the convergence properties of interior-point methods [16] and efficient algorithms have been developed with desirable global and local convergence properties.”
Convex Optimization & Euclidean Distance Geometry (2004, methodology): “1 Maximal complementarity It has been shown that contemporary interior-point methods (developed circa 1990 [89]) [42, §11] [265] [195] [187] [9] [86] for numerical solution of semidefinite programs can converge to a solution of maximal complementarity ; [111, §5] [272] [169] [95] not a vertex-soluti”
An interior penalty method for optimal control problems with state and input constraints of nonlinear systems (2016, background): “We refer the interested reader to [4] for a historical perspective on this topic.”
Control Barrier Function Based Quadratic Programs for Safety Critical Systems (2016, neutral): “Barrier functions were first utilized in optimization; see Chapter 3 of [3] for an historical account of their use in optimization.”
Reduced-basis methods applied to problems in elasticity : analysis and applications (2003, neutral): “it can then be shown [15] that as υ = (υb, υp) → 0, the solution to (7.”
Selecting additional tag SNPs for tolerating missing data in genotyping (2005, neutral): “The above LP problem can be solved in polynomial time by efficient algorithms such as the interior point method (Forsgren et al., 2002) [ 5 ].”
The interior-point revolution in optimization: History, recent developments, and lasting consequences (2004, background): “For proofs and additional details, see, for example, [36, 12 ].”
Interior point methods 25 years later (2012, methodology): “Soon after the major role played by the logarithmic barrier function [40] had been understood, a similar methodology was applied to solve quadratic [103] and nonlinear optimization problems [104] and indeed, as it was nicely pointed out by Forsgren et al. [34] " an especially appealing aspect of the”