We present a procedure for constructing a group theoretic dual problem with no duality gap to a given bounded integer programming problem. An optimal solution of this dual problem is easily determined and an optimal solution of the integer programming problem can be obtained by solving only one group optimization problem.

Owing to their low-complexity iterations, FrankWolfe (FW) solvers are well suited for various large-scale learning tasks. When block-separable constraints are present, randomized block FW (RB-FW) has been shown to further reduce complexity by updating only a fraction of coordinate blocks per iteration. To circumvent the limitations of existing methods, the present work develops step sizes for R...

We consider constrained discounted-cost Markov control processes in Bore1 spaces, with unbounded costs. Conditions are given for the constrained problem to be solvable, and also equivalent to an equality-constrained (EC) 1' inear program. In addition, it is shown that there is no duality gap between EC and its dual program EC*, and that, under additional assumptions, also EC* is solvable, so th...

Duality between N=1 supersymmetric gauge theories(Seiberg’s duality) is geometrized, in the framework of AdS/CFT correspondences. It is shown that Seiberg’s duality corresponds to monodromy of wrapped D5 branes on the homology cycles of a generalized conifold where D3 branes are located. The celebrated Ñc = Nf −Nc, Ñf = Nf rule is reproduced and a braid group structure in a sequence of dualitie...

Several combinatorial structures exhibit a duality relation that yields interesting theorems, and, sometimes, useful explanations or interpretations of results that do not concern duality explicitly. We present a common characterization of the duality relations associated with matroids, clutters (Sperner families), oriented matroids, and weakly oriented matroids. The same conditions characteriz...

We consider the problem of finding target vectors for which the nonzero duality gap exists in the problem of convex optimization. An infinitesimal approach to the duality gap analysis of convex problems is proposed. The approach is based on finding the order of smallness and the proportionality coefficient of perturbation function of the original optimization problem. We show that in case of du...

We propose a duality for N = 2 d = 3 Chern-Simons gauge theories with orthogonal gauge groups and matter in the vector representation. This duality generalizes levelrank duality for pure Chern-Simons gauge theories with orthogonal gauge groups and is reminiscent of Seiberg duality in four dimensions. We perform extensive checks by comparing partition functions of theories related by dualities. ...

We give several related versions of global Grothendieck Duality for unbounded complexes on noetherian formal schemes. The proofs, based on a nontrivial adaptation of Deligne’s method for the special case of ordinary schemes, are reasonably self-contained, modulo the Special Adjoint Functor Theorem. An alternative approach, inspired by Neeman and based on recent results about “Brown Representabi...

We clarify some ambiguous points in a derivation of duality via brane exchange using M-theory language, and propose a “proof” of duality in MQCD. Actually, duality in MQCD is rather trivial and does not need a complicated proof. The problem is how to interpret it in field theory language. We examine BPS states in N = 2 theory and find the particle correspondence under duality. In the process, w...