In this paper we derive nonlinear evolution equations associated with a class of non-convex energy functionals which can be used for correcting displacement errors in imaging data. We show a preliminary convergence result of a relaxed convexification of the non-convex optimization problem. Some properties on the behavior of the solutions of these filtering flows are studied by numerical analysi...

In this paper we present a solution method for stochastic integer problems. The method is a Benderstype algorithm that sequentially approximates the nonconvex recourse functions defined by the second stage subproblems. The presented convexification takes into account the domain that is induced by the collection of tender variables. The method is applied to a broad collection of stochastic integ...

We consider a separable complete metric space equipped with a convex combination operation. For such spaces, we identify the corresponding convexification operator and show that the invariant elements for this operator appear naturally as limits in the strong law of large numbers. It is shown how to uplift the suggested construction to work with subsets of the basic space in order to develop a ...

Devadoss asked: (1) can every polygon be convexified so that no internal visibility (between vertices) is lost in the process? Moreover, (2) does such a convexification exist, in which exactly one vertex is moved at a time (that is, using single-vertex moves)? We prove the redundancy of the " single-vertex moves " condition: an affirmative answer to (1) implies an affirmative answer to (2). Sin...

Abstract. We consider the problem of computing optimal tra c light programs for urban road intersections using tra c flow conservation laws on networks. Based on a Partial Outer Convexification approach, which has been successfully applied in the area of mixed-integer optimal control for systems of ordinary or di↵erential algebraic equations, we develop a computationally tractable two-stage sol...

We establish a semi-group solution concept for morphological differential equations, such as the mean curvature flow equation. The proposed method consists in generating flows from generalized minimizers of nonconvex energy functionals. We use relaxation and convexification to define generalized minimizers. The main part of this work consists in verification of the solution concept by comparing...

After an introduction to main ideas of semi-infinite optimization, this article surveys recent developments in theory and numerical methods for standard and generalized semi-infinite optimization problems. Particular attention is paid to connections with mathematical programs with complementarity constraints, lower level Wolfe duality, semi-smooth approaches, as well as branch and bound techniq...

We prove the bulk universality of the β-ensembles with non-convex regular analytic potentials for any β > 0. This removes the convexity assumption appeared in the earlier work [6]. The convexity condition enabled us to use the logarithmic Sobolev inequality to estimate events with small probability. The new idea is to introduce a “convexified measure” so that the local statistics are preserved ...