In this paper we present a robust conjugate duality theory for convex programming problems in the face of data uncertainty within the framework of robust optimization, extending the powerful conjugate duality technique. We first establish robust strong duality between an uncertain primal parameterized convex programming model problem and its uncertain conjugate dual by proving strong duality be...

In the paper, we describe various applications of the closedness and duality theorems of [7] and [8]. First, the strong separability of a polyhedron and a linear image of a convex set is characterized. Then, it is shown how stability conditions (known from the generalized Fenchel-Rockafellar duality theory) can be reformulated as closedness conditions. Finally, we present a generalized Lagrange...

In this paper, we consider a general composed convex optimization problem with inequality systems involving a finite number of convex constraints. We establish the strong duality between the primal problem and the Fenchel-Lagrange dual problem by a conjugate duality approach. Moreover, we obtain some new Farkas-type results for this problem by using weak and strong duality theorems. Our results...

In this paper, with the help of convex-like function, we discuss the duality theory for nonconvex semidefinite programming. Our contributions are: duality theory for the general nonconvex semidefinite programming when Slater’s condition holds; perfect duality for a special case of the nonconvex semidefinite programming for which Slater’s condition fails. We point out that the results of [2] can...

We study the optimal transport between two probability measures on the real line, where the transport plans are laws of one-step martingales. A quasi-sure formulation of the dual problem is introduced and shown to yield a complete duality theory for general marginals and measurable reward (cost) functions: absence of a duality gap and existence of dual optimizers. Both properties are shown to f...

Here we initiate an investigation of the equational classes of m– symmetric algebras endowed with two tense operators. These varieties is a generalization of tense algebras. Our main interest is the duality theory for these classes of algebras. In order to do this, we require Urquart’s duality for Ockham algebras and Goldblatt’s duality for bounded distributive lattice with operations. The dual...

Duality in the general course of human affairs seems to be a juxtaposition of complementary or opposite concepts. This frequently leads to poetical sounding uses of language, both in the common language and in the precision of mathematical theorems. Thus the duality of Projective Geometry: Two points determine a line; two lines determine a point. Gergonne first introduced the word duality in ma...

We establish a new Howe duality between a pair of two queer Lie superalgebras (q(m), q(n)). This gives a representation theoretic interpretation of a well-known combinatorial identity for Schur Q-functions. We further establish the equivalence between this new Howe duality and the Schur–Sergeev duality between q(n) and a central extension H̃k of the hyperoctahedral group Hk. We show that the zer...

In this paper, we will define and study amenability of Hopf C-algebras as well as that of Fourier duality. 1991 AMS Mathematics Classification number: 46L55, 46L05