Since T-duality has been proved only perturbatively and most of the heterotic states map into solitonic, non-perturbative, type II states, the 6-dimensional string-string duality between the heterotic string and the type II string is not sufficient to prove the S-duality of the former, in terms of the known T-duality of the latter. We nevertheless show in detail that the perturbative T-duality,...

Cosmologically stabilizing radion along with the dilaton is one of the major concerns of low energy string theory. One can hope that T and S dualities can provide a plausible answer. In this work we study the impact of S and T duality invariances on dilaton gravity. We have shown various instances where physically interesting models arise as a result of imposing the mentioned invariances. In pa...

It is well known that the duality theory for linear programming (LP) is powerful and elegant and lies behind algorithms such as simplex and interior-point methods. However, the standard Lagrangian for nonlinear programs requires constraint qualifications to avoid duality gaps. Semidefinite linear programming (SDP) is a generalization of LP where the nonnegativity constraints are replaced by a s...

Bounded linear regularity, the strong conical hull intersection property (strong CHIP), and the conical hull intersection property (CHIP) are properties of a collection of finitely many closed convex intersecting sets in Euclidean space. It was shown recently that these properties are fundamental in several branches of convex optimization, including convex feasibility problems, error bounds, Fe...

We consider the problem of minimizing a convex function over a subset of R that is not necessarily convex (minimization of a convex function over the integer points in a polytope is a special case). We define a family of duals for this problem and show that, under some natural conditions, strong duality holds for a dual problem in this family that is more restrictive than previously considered ...

This paper presents a set of complete solutions and optimality conditions for a nonconvex quadratic-exponential optimization problem. By using the canonical duality theory developed by the first author, the nonconvex primal problem in n-dimensional space can be converted into an one-dimensional canonical dual problem with zero duality gap, which can be solved easily to obtain all dual solutions...

A full duality gives us a natural dual equivalence between a quasi-variety generated by a finite algebra and a class of structured topological spaces. There are many well-known examples of full dualities: Stone’s duality for Boolean algebras [12], Priestley’s duality for distributive lattices [11], and the Hofmann, Mislove, Stralka duality for semilattices [6]. A finite algebra M is called full...

We find the explicit T-duality transformation in the phase space formulation of the N = (1, 1) sigma model. We also show that the T-duality transformation is a symplectomorphism and it is an element of O(d, d). Further, we find the explicit T-duality transformation of a generalized complex structure. We also show that the extended supersymmetry of the sigma model is preserved under the T-duality.

In this contribution we present the superfield T-duality rules relating type IIA and type IIB supergravity potentials for the case when both type IIA and type IIB superspaces have (at least) one isometry direction. We also give a brief review of T–duality and discuss the main steps of our approach to the derivation of the superfield T–duality rules, including the treatment of T-duality as an op...

In this paper, the existence of an optimal path and its convergence to the optimal set of a primal problem of minimizing an extended real-valued function are established via a generalized augmented Lagrangian and corresponding generalized augmented Lagrangian problems, in which no convexity is imposed on the augmenting function. These results further imply a zero duality gap property between th...