We first establish sufficient conditions ensuring strong duality for cone constrained nonconvex optimization problems under a generalized Slater-type condition. Such conditions allow us to cover situations where recent results cannot be applied. Afterwards, we provide a new complete characterization of strong duality for a problem with a single constraint: showing, in particular, that strong du...

We give a bundle method for constrained convex optimization. Instead of using penalty functions, it shifts iterates towards feasibility, by way of a Slater point, assumed to be known. Besides, the method accepts an oracle delivering function and subgradient values with unknown accuracy. Our approach is motivated by a number of applications in column generation, in which constraints are positive...

In 1959 Gallai [5] showed that the vertex independence number and the vertex covering number of a graph G = (V,E) sum to |V |. Over the last twenty years, many results similar to Gallai’s Theorem have been observed [3]. These theorems are referred to as “Gallai Theorems” and usually have the form: α+ β = n. Slater [17] described several graph subset parameters using linear programs (LP) and int...

The many-body theory of degenerate systems is described in detail. More generally, this theory applies to systems with an initial state that cannot be described by a single Slater determinant. The double-source (or closed-time-path) formalism of nonequilibrium quantum field theory is used to derive an expression for the average value of a product of interacting fields when the initial state is ...

In previous work the authors considered the asymmetric simple exclusion process on the integer lattice in the case of step initial condition, particles beginning at the positive integers. There it was shown that the probability distribution for the position of an individual particle is given by an integral whose integrand involves a Fredholm determinant. Here we use this formula to obtain three...

We study the differentiable structure and the homotopy type of some spaces related to the Grassmannian of closed linear subspaces of an infinite dimensional Hilbert space, such as the space of Fredholm pairs, the Grassmannian of compact perturbations of a given space, and the essential Grassmannians. We define a determinant bundle over the space of Fredholm pairs. We lift the composition of Fre...

In this paper we investigate the existence of positive solutions to the following Schrödinger-Poisson-Slater system