Search results for "optimization"

showing 10 items of 2824 documents

The Fixed Point Property in Banach Spaces with the NUS-Property

1997

Abstract In this paper, we show that the weak nearly uniform smooth Banach spaces have the fixed point property for nonexpansive mappings.

Discrete mathematicsMathematics::Functional AnalysisApproximation propertyApplied MathematicsEberlein–Šmulian theoremMathematics::Optimization and ControlBanach spaceBanach manifoldFixed-point propertyOpial propertyInterpolation spaceLp spaceAnalysisMathematicsJournal of Mathematical Analysis and Applications
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Fixed point theory for a class of generalized nonexpansive mappings

2011

AbstractIn this paper we introduce two new classes of generalized nonexpansive mapping and we study both the existence of fixed points and their asymptotic behavior.

Discrete mathematicsMathematics::Functional AnalysisClass (set theory)Nonexpansive mappingApplied MathematicsMathematics::Optimization and ControlFixed-point theoremFixed pointFixed pointAnalysisDemiclosedness principleMathematicsJournal of Mathematical Analysis and Applications
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Closedness and lower semicontinuity of positive sesquilinear forms

2009

The relationship between the notion of closedness, lower semicontinuity and completeness (of a quotient) of the domain of a positive sesquilinear form defined on a subspace of a topological vector space is investigated and sufficient conditions for their equivalence are given.

Discrete mathematicsMathematics::Functional AnalysisPure mathematicsMathematics::Operator AlgebrasSesquilinear formGeneral MathematicsMathematics::Optimization and ControlMathematics::General TopologyClosedness Semicontinuity Sesquilinear formsDomain (mathematical analysis)Topological vector spaceSettore MAT/05 - Analisi MatematicaAlgebra over a fieldCompleteness (statistics)Equivalence (measure theory)Subspace topologyQuotientMathematicsRendiconti del Circolo Matematico di Palermo
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Hoffman's Error Bound, Local Controllability, and Sensitivity Analysis

2000

Our aim is to present sufficient conditions ensuring Hoffman's error bound for lower semicontinuous nonconvex inequality systems and to analyze its impact on the local controllability, implicit function theorem for (non-Lipschitz) multivalued mappings, generalized equations (variational inequalities), and sensitivity analysis and on other problems like Lipschitzian properties of polyhedral multivalued mappings as well as weak sharp minima or linear conditioning. We show how the information about our sufficient conditions can be used to provide a computable constant such that Hoffman's error bound holds. We also show that this error bound is nothing but the classical Farkas lemma for linear …

Discrete mathematicsMaxima and minimaControllabilityLinear inequalityControl and OptimizationApplied MathematicsErgodicityVariational inequalityApplied mathematicsConstant (mathematics)Farkas' lemmaImplicit function theoremMathematicsSIAM Journal on Control and Optimization
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Optimal paths in weighted timed automata

2004

AbstractWe consider the optimal-reachability problem for a timed automaton with respect to a linear cost function which results in a weighted timed automaton. Our solution to this optimization problem consists of reducing it to computing (parametric) shortest paths in a finite weighted directed graph. We call this graph a parametric sub-region graph. It refines the region graph, a standard tool for the analysis of timed automata, by adding the information which is relevant to solving the optimal-reachability problem. We present an algorithm to solve the optimal-reachability problem for weighted timed automata that takes time exponential in O(n(|δ(A)|+|wmax|)), where n is the number of clock…

Discrete mathematicsModel checkingHybrid systemsOptimization problemGeneral Computer ScienceComputer scienceOptimal reachabilityTimed automatonBüchi automatonDirected graphTheoretical Computer ScienceAutomatonCombinatoricsDeterministic automatonReachabilityShortest path problemState spaceAutomata theoryGraph (abstract data type)Two-way deterministic finite automatonTimed automataAlgorithmComputer Science::Formal Languages and Automata TheoryComputer Science(all)Mathematics
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Some properties of [tr(Q2p)]12p with application to linear minimax estimation

1990

Abstract A nondifferentiable minimization problem is considered which occurs in linear minimax estimation. This problem is solved by replacing the nondifferentiable maximal eigenvalue of a real nonnegative definite matrix Q with [tr( Q 2 p )] 1/2 p . It is shown that any descent algorithm with inexact step-length rule can be used to obtain linear minimax estimators for the parameter vector of a parameter-restricted linear model.

Discrete mathematicsNumerical AnalysisAlgebra and Number TheoryMinimization problemLinear modelMathematics::Optimization and ControlMinimaxMinimax approximation algorithmMatrix (mathematics)Discrete Mathematics and CombinatoricsGeometry and TopologyMinimax estimatorDescent algorithmEigenvalues and eigenvectorsMathematicsLinear Algebra and its Applications
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Fixed points and completeness on partial metric spaces

2015

Recently, Suzuki [T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc. 136 (2008), 1861-1869] proved a fixed point theorem that is a generalization of the Banach contraction principle and characterizes the metric completeness. Paesano and Vetro [D. Paesano and P. Vetro, Suzuki's type characterizations of completeness for partial metric spaces and fixed points for partially ordered metric spaces, Topology Appl., 159 (2012), 911-920] proved an analogous fixed point result for a selfmapping on a partial metric space that characterizes the partial metric 0-completeness. In this paper we prove a fixed point result for a new class of…

Discrete mathematicsNumerical AnalysisPartial metric 0-completeneControl and OptimizationAlgebra and Number TheoryPartial metric spaceInjective metric spaceOrdered partial metric spaceEquivalence of metricsConvex metric spaceIntrinsic metricMetric spaceSettore MAT/05 - Analisi MatematicaSuzuki fixed point theoremCompleteness (order theory)Metric (mathematics)Discrete Mathematics and CombinatoricsMetric mapFixed and common fixed pointAnalysisMathematicsMiskolc Mathematical Notes
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Property (gab) through localized SVEP

2015

In this article we study the property (gab) for a bounded linear operator T 2 L(X) on a Banach space X which is a stronger variant of Browder's theorem. We shall give several characterizations of property (gab). These characterizations are obtained by using typical tools from local spectral theory. We also show that property (gab) holds for large classes of operators and prove the stability of property (gab) under some commuting perturbations. 2010 Mathematics Subject Classication. Primary 47A10, 47A11; Secondary 47A53, 47A55.

Discrete mathematicsNumerical AnalysisPure mathematicsControl and OptimizationSpectral theoryProperty (philosophy)Property (gab) local spectral subspaces Browder type theorems.Applied Mathematics010102 general mathematicsBanach space010103 numerical & computational mathematics01 natural sciencesStability (probability)Bounded operatorSettore MAT/05 - Analisi Matematica0101 mathematicsAnalysisMathematics
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An exact and efficient approach for computing a cell in an arrangement of quadrics

2006

AbstractWe present an approach for the exact and efficient computation of a cell in an arrangement of quadric surfaces. All calculations are based on exact rational algebraic methods and provide the correct mathematical results in all, even degenerate, cases. By projection, the spatial problem is reduced to the one of computing planar arrangements of algebraic curves. We succeed in locating all event points in these arrangements, including tangential intersections and singular points. By introducing an additional curve, which we call the Jacobi curve, we are able to find non-singular tangential intersections. We show that the coordinates of the singular points in our special projected plana…

Discrete mathematicsPure mathematicsArrangementsControl and OptimizationFunction field of an algebraic varietyAlgebraic curvesMathematicsofComputing_NUMERICALANALYSISComputational geometryComputer Science ApplicationsComputational MathematicsComputational Theory and MathematicsJacobian curveAlgebraic surfaceComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONReal algebraic geometryAlgebraic surfacesExact algebraic computationAlgebraic functionGeometry and TopologyAlgebraic curveAlgebraic numberRobustnessMathematicsSingular point of an algebraic varietyComputational Geometry
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Farkas-Minkowski systems in semi-infinite programming

1981

The Farkas-Minkowski systems are characterized through a convex cone associated to the system, and some sufficient conditions are given that guarantee the mentioned property. The role of such systems in semi-infinite programming is studied in the linear case by means of the duality, and, in the nonlinear case, in connection with optimality conditions. In the last case the property appears as a constraint qualification.

Discrete mathematicsPure mathematicsNonlinear systemControl and OptimizationApplied MathematicsMinkowski spaceSecond-order cone programmingDuality (optimization)Constraint satisfactionSemi-infinite programmingMathematicsApplied Mathematics & Optimization
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