Report The aim of this work is to make some investigations concerning duality for mul-tiobjective optimization problems. In order to do this we study first the duality for scalar optimization problems by using the conjugacy approach. This allows us to attach three different dual problems to a primal one. We examine the relations between the optimal objective values of the duals and verify, unde...

Given a hyperplane arrangement in an affine space equipped with a linear functional, we define two finite-dimensional, noncommutative algebras, both of which are motivated by the geometry of hypertoric varieties. We show that these algebras are Koszul dual to each other, and that the roles of the two algebras are reversed by Gale duality. We also study the centers and representation categories ...

2 Algebraic preliminaries 4 2.1 Notations and conventions . . . . . . . . . . . . . . . . . . . . 4 2.2 Duality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2.1 Local Duality . . . . . . . . . . . . . . . . . . . . . . . 5 2.2.2 Global Duality . . . . . . . . . . . . . . . . . . . . . . 6 2.3 Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.4 Prelimin...

A way of covariantizing duality symmetric actions is described. The presence of self–dual fields or, in more general case, duality–symmetric fields in field–theoretical and string models reflects their duality properties whose extreme importance for understanding a full quantum theory has been appreciated during an impetuous development of the duality field happened during last few years. The k...

we study the notion of harmonicity in the sense of symplectic geometry, and investigate the geometric properties of harmonic thom forms and distributional thom currents, dual to different types of submanifolds. we show that the harmonic thom form associated to a symplectic submanifold is nowhere vanishing. we also construct symplectic smoothing operators which preserve the harmonicity of distri...

In this letter we implement a recently proposed spacetime duality approach to dualize a two dimensional, Abelian, gauge field theory, which has no dual version under p–duality. Our result suggests that spacetime duality spans a new, wider, class of dual theories, which cannot be related one to another by p–duality transformations.