The zero duality gap that underpins the duality theory is one of the central ingredients in optimisation. In convex programming, it means that the optimal values of a given convex program and its associated dual program are equal. It allows, in particular, the development of efficient numerical schemes. However, the zero duality gap property does not always hold even for finite dimensional prob...

Duality is an important notion for nonlinear programming (NLP). It provides a theoretical foundation for many optimization algorithms. Duality can be used to directly solve NLPs as well as to derive lower bounds of the solution quality which have wide use in other high-level search techniques such as branch and bound. However, the conventional duality theory has the fundamental limit that it le...

We prove a duality for factorization homology which generalizes both usual Poincaré duality for manifolds and Koszul duality for En-algebras. The duality has application to the Hochschild homology of associative algebras and enveloping algebras of Lie algebras. We interpret our result at the level of topological quantum field theory.

We introduce the notion of hyper-self-duality for Bose-Mesner algebras as a strengthening of formal self-duality. LetM denote a Bose-Mesner algebra on a finite nonempty set X . Fix p ∈ X , and letM∗ and T denote respectively the dual Bose-Mesner algebra and the Terwilliger algebra ofMwith respect to p. By a hyper-duality ofM, we mean an automorphism ψ of T such that ψ(M) =M∗, ψ(M∗) =M; ψ2(A) = ...

I ascribe the origin of Bloom-Gilman duality in DIS to a separation of scales between the hard subprocess and soft resonance formation. The success of duality indicates that the subprocesses of exclusive form factors are the same as in DIS. The observed dominance of the longitudinal structure function at large x in πN → µ + µ − X can explain why local duality works for DIS with a pion target. T...

We study strong-weak coupling duality (S-duality) in N=4 supersymmetric nonAbelian Yang-Mills theories. These theories arise naturally as the low-energy limit of four-dimensional toroidal compactifications of the heterotic string. Firstly, we define the free energy in the presence of electric and magnetic fluxes using ’t Hooft’s prescription, i.e. through functional integrals at finite volume i...

Propounding a general categorical framework for the extension of dualities, we present new proof de Vries Duality Theorem category KHaus compact Hausdorff spaces and their continuous maps, as an restricted Stone duality. Then, applying dualization to duality, give alternative duality Tych Tychonoff that was provided by Bezhanishvili, Morandi Olberding. In process doing so, obtain theorems both ...