Nonlinear programming without a penalty function

By Roger Fletcher, Sven Leyffer. Mathematical programming, 2002

967 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/49b5a0ffbdcf33451858f5757e6fa34074de388a

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In Computational Theory and Mathematics

In Control and Systems Engineering

In Numerical Analysis

Citations in the corpus

On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming (2006, methodology): “On the other hand, Fletcher and Leyffer [14] recently proposed filter methods, offering an alternative to merit functions, as a tool to guarantee global convergence in algorithms for nonlinear programming.”
Optimization by Direct Search: New Perspectives on Some Classical and Modern Methods (2003, methodology): “A strategy similar in spirit is used in Audet and Dennis [12], where a filter method inspired by that of Fletcher and Leyffer [108] is applied.”
Surrogate-based Analysis and Optimization (2005, background): “In particular, Fletcher and Leyffer [95] recently presented a so-called filter approach that does not require estimating a potentially troublesome penalty or barrier parameter.”
Complementarity constraints as nonlinear equations: Theory and numerical experience (2006, methodology): “The filter accepts a trial point whenever the objective or the constraint violation is improved compared with all previous iterates [14, 15, 18].”
Global Convergence of a Trust-Region SQP-Filter Algorithm for General Nonlinear Programming (2002, methodology): “Note that we have chosen here to reduce the infinity norm of the constraint violation, but we could equally well consider other norms, such as 1 or 2 , in which case the methods of Fletcher and Leyffer [17] or of El-Hallabi and Tapia [14] and Dennis, El-Alem, and Williamson [10], respectively, can b”
Mixed Variable Optimization of a Load-Bearing Thermal Insulation System Using a Filter Pattern Search Algorithm (2004, methodology): “Proofs of convergence to a first-order stationary point are given in Fletcher et al. (1998) for SQP and Fletcher et al.”
Line Search Filter Methods for Nonlinear Programming: Motivation and Global Convergence (2005, methodology): “Instead, following Fletcher and Leyffer’s original idea, the trial point xk(αk,l) is accepted if it improves feasibility, i.e. if θ(xk(αk,l)) θ(xk), or if it improves the objective function, i.e. if f(xk(αk,l)) f(xk).”
Interior Methods for Nonlinear Optimization (2002, methodology): “A quite different procedure for forcing convergence is to use a filter, first proposed in [36] in the context of SQP methods.”
A Pattern Search Filter Method for Nonlinear Programming without Derivatives (2001, methodology): “Filter algorithms were introduced by Fletcher and Leyffer [ 14 ] as a way to globalize sequential linear and quadratic programming (SLP and SQP) without using any merit function that would require a troublesome parameter to be provided by the user for weighting the relative merits of improving feasi”
Advances in simultaneous strategies for dynamic process optimization (2002, methodology): “Termed the lter approach, this method was recently developed in a trust region context for SQP and other nonlinear programming algorithms [23].”
An interior algorithm for nonlinear optimization that combines line search and trust region steps (2006, methodology): “Other approaches include the use of 1 or 2 penalizations of the constraints, which provide regularization [16] [24], and the use of a feasibility restoration phase [15] [27].”
MINLP Solver Software (2011, methodology): “In this category we have alphaBB, AlphaECP, AOA, BARON, DICOPT, LaGO, and LindoGlobal.”
A Primal-Dual Interior Point Method for Optimal Power Flow Dispatching (2002, methodology): “Definition 2 [ 20 ]: A filter is a list of pairs such that no pair dominates any other.”
A survey of numerical methods for nonlinear semidefinite programming (2015, methodology): “The filter methods were first introduced by Fletcher and Leyffer [19] for nonlinear optimization problems.”
Local Convergence of SQP Methods for Mathematical Programs with Equilibrium Constraints (2006, methodology): “The solver snopt [12] uses an elastic mode that relaxes the linearizations of the QP; filter [9] has a restoration phase.”