10,720 research outputs found
Geometric Duality for Convex Vector Optimization Problems
Geometric duality theory for multiple objective linear programming problems
turned out to be very useful for the development of efficient algorithms to
generate or approximate the whole set of nondominated points in the outcome
space. This article extends the geometric duality theory to convex vector
optimization problems.Comment: 21 page
Empirical properties of duality theory
This research examines selected empirical properties of duality relationships. Monte Carlo experiments indicate that Hessian matrices estimated from the normalised unrestricted profit, restricted profit and production functions yield conflicting results in the presence of measurement error and low relative price variability. In particular, small amounts of measurement error in quantity variables can translate into large errors in uncompensated estimates calculated via restricted and unrestricted profit and production functions. These results emphasise the need for high quality data when estimating empirical models in order to accurately determine dual relationships implied by economic theory.Research Methods/ Statistical Methods,
An Algebraic Duality Theory for Multiplicative Unitaries
Multiplicative Unitaries are described in terms of a pair of commuting shifts
of relative depth two. They can be generated from ambidextrous Hilbert spaces
in a tensor C*-category. The algebraic analogue of the Takesaki-Tatsuuma
Duality Theorem characterizes abstractly C*-algebras acted on by unital
endomorphisms that are intrinsically related to the regular representation of a
multiplicative unitary. The relevant C*-algebras turn out to be simple and
indeed separable if the corresponding multiplicative unitaries act on a
separable Hilbert space. A categorical analogue provides internal
characterizations of minimal representation categories of a multiplicative
unitary. Endomorphisms of the Cuntz algebra related algebraically to the
grading are discussed as is the notion of braided symmetry in a tensor
C*-category.Comment: one reference adde
On Lagrangian Duality in Vector Optimization. Applications to the linear case.
The paper deals with vector constrained extremum problems. A separation scheme is recalled; starting from it, a vector Lagrangian duality theory is developed. The linear duality due to Isermann can be embedded in this separation approach. Some classical applications are extended to the multiobjective framework in the linear case, exploiting the duality theory of Isermann.Vector Optimization, Separation, Image Space Analysis, Lagrangian Duality, Set-Valued Function.
Applications of duality theory to cousin complexes
We use the anti-equivalence between Cohen-Macaulay complexes and coherent
sheaves on formal schemes to shed light on some older results and prove new
results. We bring out the relations between a coherent sheaf M satisfying an
S_2 condition and the lowest cohomology N of its "dual" complex. We show that
if a scheme has a Gorenstein complex satisfying certain coherence conditions,
then in a finite \'etale neighborhood of each point, it has a dualizing
complex. If the scheme already has a dualizing complex, then we show that the
Gorenstein complex must be a tensor product of a dualizing complex and a vector
bundle of finite rank. We relate the various results in [S] on Cousin complexes
to dual results on coherent sheaves on formal schemes.Comment: 40 pages. Substantially different from earlier version(s). To appear
in Journal of Algebr
APPLICATIONS OF DUALITY THEORY TO AGRICULTURE
Research Methods/ Statistical Methods,
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