Search results for "Vector-valued function"

showing 2 items of 12 documents

Multifunctions determined by integrable functions

2019

Integral properties of multifunctions determined by vector valued functions are presented. Such multifunctions quite often serve as examples and counterexamples. In particular it can be observed that the properties of being integrable in the sense of Bochner, McShane or Birkhoff can be transferred to the generated multifunction while Henstock integrability does not guarantee it.

Pure mathematicsPositive multifunctionIntegrable systemApplied Mathematicsselection02 engineering and technologymultifunction determined by a functionTheoretical Computer ScienceFunctional Analysis (math.FA)28B20 26E25 26A39 28B05 46G10 54C60 54C65Mathematics - Functional AnalysisPositive multifunction gauge integral selection multifunction determined by a function measure theory.measure theorySettore MAT/05 - Analisi MatematicaArtificial Intelligence020204 information systemsgauge integral0202 electrical engineering electronic engineering information engineeringFOS: Mathematics020201 artificial intelligence & image processingVector-valued functionSoftwareCounterexampleMathematics
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Exact extension of the DIRECT algorithm to multiple objectives

2019

The direct algorithm has been recognized as an efficient global optimization method which has few requirements of regularity and has proven to be globally convergent in general cases. direct has been an inspiration or has been used as a component for many multiobjective optimization algorithms. We propose an exact and as genuine as possible extension of the direct method for multiple objectives, providing a proof of global convergence (i.e., a guarantee that in an infinite time the algorithm becomes everywhere dense). We test the efficiency of the algorithm on a nonlinear and nonconvex vector function. peerReviewed

ta113Computer scienceDirect methodta111multi-objective optimisationExtension (predicate logic)algorithmsMulti-objective optimizationmonitavoiteoptimointiNonlinear systemComponent (UML)Convergence (routing)algoritmitGlobal optimizationVector-valued functionAlgorithm
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