Search results for "Strong duality"

showing 5 items of 5 documents

Introduction to General Duality Theory for Multi-Objective Optimization

1992

This is intended as a comprehensive introduction to the duality theory for vector optimization recently developed by C. Malivert and the present author [3]. It refers to arbitrarily given classes of mappings (dual elements) and extends the general duality theory proposed for scalar optimization by E. Balder, S. Kurcyusz and the present author [1] and P. Lindberg.

AlgebraMathematical optimizationVector optimizationStrong dualityWolfe dualityDuality (optimization)Multi-objective optimizationMathematicsScalar optimization
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The hidden group structure of quantum groups: strong duality, rigidity and preferred deformations

1994

A notion of well-behaved Hopf algebra is introduced; reflexivity (for strong duality) between Hopf algebras of Drinfeld-type and their duals, algebras of coefficients of compact semi-simple groups, is proved. A hidden classical group structure is clearly indicated for all generic models of quantum groups. Moyal-product-like deformations are naturally found for all FRT-models on coefficients andC∞-functions. Strong rigidity (H bi 2 ={0}) under deformations in the category of bialgebras is proved and consequences are deduced.

Classical groupPure mathematicsQuantum groupDeformation theoryLie groupStatistical and Nonlinear PhysicsHopf algebra17B37Algebra81R50Compact groupMathematics::Quantum AlgebraStrong dualityDual polyhedron16W30Mathematical PhysicsMathematics
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On the duality between mechanistic learners and what it is they learn

1993

All previous work in inductive inference and theoretical machine learning has taken the perspective of looking for a learning algorithm that successfully learns a collection of functions. In this work, we consider the perspective of starting with a set of functions, and considering the collection of learning algorithms that are successful at learning the given functions. Some strong dualities are revealed.

Computer Science::Machine Learningbusiness.industryPerspective (graphical)Duality (mathematics)Multi-task learningInductive reasoningMachine learningcomputer.software_genreRecursive functionsStrong dualityArtificial intelligenceSet (psychology)businesscomputerMathematics
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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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The Radon-Nikodym Theorem. Duality

1998

The band in M( ℜ) generated by a particular real measure μ can be characterized in various ways.

Radon–Nikodym theoremsymbols.namesakePure mathematicsFenchel's duality theoremsymbolsKronecker's theoremStrong dualityDuality (optimization)Danskin's theoremMeasure (mathematics)Poincaré dualityMathematics
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