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# Filter (higher-order function)

About: Filter (higher-order function) is a research topic. Over the lifetime, 100 publications have been published within this topic receiving 2460 citations.

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TL;DR: The aim of the present work is to promote global convergence without the need to use a penalty function, so a new concept of a “filter” is introduced which allows a step to be accepted if it reduces either the objective function or the constraint violation function.

Abstract: In this paper the solution of nonlinear programming problems by a Sequential Quadratic Programming (SQP) trust-region algorithm is considered. The aim of the present work is to promote global convergence without the need to use a penalty function. Instead, a new concept of a “filter” is introduced which allows a step to be accepted if it reduces either the objective function or the constraint violation function. Numerical tests on a wide range of test problems are very encouraging and the new algorithm compares favourably with LANCELOT and an implementation of Sl1QP.

879 citations

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TL;DR: Under mild assumptions it is shown that every limit point of the sequence of iterates generated by the algorithm is feasible, and that there exists at least one limit point that is a stationary point for the problem under consideration.

Abstract: Line search methods are proposed for nonlinear programming using Fletcher and Leyffer's filter method [Math. Program., 91 (2002), pp. 239--269], which replaces the traditional merit function. Their global convergence properties are analyzed. The presented framework is applied to active set sequential quadratic programming (SQP) and barrier interior point algorithms. Under mild assumptions it is shown that every limit point of the sequence of iterates generated by the algorithm is feasible, and that there exists at least one limit point that is a stationary point for the problem under consideration. A new alternative filter approach employing the Lagrangian function instead of the objective function with identical global convergence properties is briefly discussed.

396 citations

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TL;DR: It is proved that, under reasonable conditions and for every possible choice of the starting point, the sequence of iterates has at least one first-order critical accumulation point.

Abstract: A trust-region SQP-filter algorithm of the type introduced by Fletcher and Leyffer [Math. Program., 91 (2002), pp. 239--269] that decomposes the step into its normal and tangential components allows for an approximate solution of the quadratic subproblem and incorporates the safeguarding tests described in Fletcher, Leyffer, and Toint [On the Global Convergence of an SLP-Filter Algorithm, Technical Report 98/13, Department of Mathematics, University of Namur, Namur, Belgium, 1998; On the Global Convergence of a Filter-SQP Algorithm, Technical Report 00/15, Department of Mathematics, University of Namur, Namur, Belgium, 2000] is considered. It is proved that, under reasonable conditions and for every possible choice of the starting point, the sequence of iterates has at least one first-order critical accumulation point.

273 citations

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TL;DR: A graphical Filter/Flow representation of Boolean queries was designed to provide users with an interface that visually conveys the meaning of the Boolean operators (AND, OR, and NOT) by implementing a graphical interface prototype that uses the metaphor of water flowing through filters.

Abstract: One of the powerful applications of Boolean expression is to allow users to extract relevant information from a database. Unfortunately, previous research has shown that users have difficulty specifying Boolean queries. In an attempt to overcome this limitation, a graphical Filter/Flow representation of Boolean queries was designed to provide users with an interface that visually conveys the meaning of the Boolean operators (AND, OR, and NOT). This was accomplished by implementing a graphical interface prototype that uses the metaphor of water flowing through filters. Twenty subjects having no experience with Boolean logic participated in an experiment comparing the Boolean operations represented in the Filter/Flow interface with a text-only SQL interface. The subjects independently performed five comprehension tasks and five composition tasks in each of the interfaces. A significant difference (p < 0.05) in the total number of correct queries in each of the comprehension and composition tasks was found favoring Filter/Flow. © 1993 John Wiley & Sons, Inc.

161 citations

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25 Mar 2004TL;DR: A new high-level programming language for programming applications with hard real-time constraints, called xGiotto, based on the LET assumption, which accommodates also asynchronous events through a mechanism called event scoping.

Abstract: We present a new high-level programming language, called xGiotto, for programming applications with hard real-time constraints Like its predecessor, xGiotto is based on the LET (logical execution time) assumption: the programmer specifies when the outputs of a task become available, and the compiler checks if the specification can be implemented on a given platform However, while the predecessor language xGiotto was purely time-triggered, xGiotto accommodates also asynchronous events Indeed, through a mechanism called event scoping, events are the main structuring principle of the new language The xGiotto compiler and run-time system implement event scoping through a tree-based event filter The compiler also checks programs for determinism (absence of race conditions)

70 citations