Search results for "Proper convex function"

showing 6 items of 6 documents

Non absolutely convergent integrals of functions taking values in a locally convex space

2006

Properties of McShane and Kurzweil-Henstock integrable functions taking values in a locally convex space are considered and the relations with other integrals are studied. A convergence theorem for the Kurzweil-Henstock integral is given

Convex analysisMcShane integralGeneral MathematicsMathematical analysisConvex setProper convex functionSubderivativeKurzweil-Henstock integralChoquet theory28B05McShaneintegral Pettis integralSettore MAT/05 - Analisi MatematicaLocally convex topological vector spacelocally convex spacesPettis integralConvex combinationAbsolutely convex setMathematics46G10
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Riemann type integrals for functions taking values in a locally convex space

2006

The McShane and Kurzweil-Henstock integrals for functions taking values in a locally convex space are defined and the relations with other integrals are studied. A characterization of locally convex spaces in which Henstock Lemma holds is given.

Convex analysisPure mathematicsGeneral MathematicsMathematical analysisMathematics::Classical Analysis and ODEsProper convex functionConvex setSubderivativeChoquet theoryLocally convex topological vector spaceConvex combinationPettis integral McShane integral Kurzweil-Henstock integral locally convex spacesAbsolutely convex setMathematicsCzechoslovak Mathematical Journal
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Convex bodies and convexity on Grassmann cones

1962

CombinatoricsConvex analysisMixed volumeGeneral MathematicsConvex polytopeProper convex functionConvex setGeometrySubderivativeChoquet theoryConvexityMathematicsArchiv der Mathematik
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Approximate convex hull of affine iterated function system attractors

2012

International audience; In this paper, we present an algorithm to construct an approximate convex hull of the attractors of an affine iterated function system (IFS). We construct a sequence of convex hull approximations for any required precision using the self-similarity property of the attractor in order to optimize calculations. Due to the affine properties of IFS transformations, the number of points considered in the construction is reduced. The time complexity of our algorithm is a linear function of the number of iterations and the number of points in the output convex hull. The number of iterations and the execution time increases logarithmically with increasing accuracy. In additio…

Discrete mathematicsConvex hull0209 industrial biotechnologyGeneral MathematicsApplied Mathematics010102 general mathematicsProper convex functionConvex setMathematicsofComputing_GENERALGeneral Physics and AstronomyStatistical and Nonlinear Physics02 engineering and technology[ INFO.INFO-GR ] Computer Science [cs]/Graphics [cs.GR]01 natural sciences[INFO.INFO-GR]Computer Science [cs]/Graphics [cs.GR]020901 industrial engineering & automationAffine hullTheoryofComputation_ANALYSISOFALGORITHMSANDPROBLEMCOMPLEXITYConvex polytopeOutput-sensitive algorithmConvex combination0101 mathematicsConvex conjugateMathematics
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On some close to convex functions with negative coefficients

2007

In this paper we propose for study a class of close to convex functions with negative coefficients defined by using a modified Salagean operator. .

Convex hullConvex analysisPure mathematicsGeneral MathematicsMathematical analysisConvex optimizationConvex setProper convex functionConvex combinationSubderivativeConvex conjugateMathematicsFilomat
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Convex Duality in Stochastic Optimization and Mathematical Finance

2011

This paper proposes a general duality framework for the problem of minimizing a convex integral functional over a space of stochastic processes adapted to a given filtration. The framework unifies many well-known duality frameworks from operations research and mathematical finance. The unification allows the extension of some useful techniques from these two fields to a much wider class of problems. In particular, combining certain finite-dimensional techniques from convex analysis with measure theoretic techniques from mathematical finance, we are able to close the duality gap in some situations where traditional topological arguments fail.

Convex analysisMathematical optimizationDuality gapGeneral MathematicsConvex optimizationProper convex functionDuality (optimization)Strong dualityWolfe dualityPerturbation functionManagement Science and Operations ResearchComputer Science ApplicationsMathematicsMathematics of Operations Research
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