We study the existence theory for parabolic variational inequalities in weighted L spaces with respect to excessive measures associated with a transition semigroup. We characterize the value function of optimal stopping problems for finite and infinite dimensional diffusions as a generalized solution of such a variational inequality. The weighted L setting allows us to cover some singular cases...

In this paper, we study self-avoiding walks of a given length on a graph. We consider a formulation of this problem as a binary linear program. We analyze the polyhedral structure of the underlying polytope and describe valid inequalities. Proofs for their facial properties for certain special cases are given. In a variation of this problem one is interested in optimal configurations, where an ...

We present mixed integer programming approaches for optimally solving a combinatorial optimization problem arising in network design with additional quality of service constraints. The rooted delayand delay-variation-constrained Steiner tree problem asks for a cost-minimal Steiner tree satisfying delay-constraints from source to terminals and a maximal variation-bound between particular termina...

In this paper, we establish moderate deviations for the chemical distance in Bernoulli percolation. The chemical distance D(x, y) between two points is the length of the shortest open path between these two points. Thus, we study the size of random fluctuations around the mean value, and also the asymptotic behavior of this mean value. The estimates we obtain improve our knowledge of the conver...

We present a method of lifting linear inequalities for the flag f -vector of polytopes to higher dimensions. Known inequalities that can be lifted using this technique are the non-negativity of the toric g-vector and that the simplex minimizes the cd-index. We obtain new inequalities for 6-dimensional polytopes. In the last section we present the currently best known inequalities for dimensions...

This paper studies the complexity of solving two classes of non-cooperative games in a distributed manner in which the players communicate with a set of system nodes over noisy communication channels. The complexity of solving each game class is defined as the minimum number of iterations required to find a Nash equilibrium (NE) of any game in that class with ǫ accuracy. First, we consider the ...

As a consequence of the Bochner formula for Bismut connection acting on gradients, we show sharp universal Poincaré and log-Sobolev inequalities along solutions to generalized Ricci flow. Using two-form potential define twisted spacetime which determines an adapted Brownian motion frame bundle, yielding Malliavin gradient path space. We this operator, leading characterizations flow in terms typ...

we introduce variational inequality problems on hilbert $c^*$-modules and we prove several existence results for variational inequalities defined on closed convex sets. then relation between variational inequalities, $c^*$-valued metric projection and fixed point theory  on  hilbert $c^*$-modules is studied.

Robust Solution of Mixed Complementarity Problems Steven P Dirkse Under the Supervision of Associate Professor Michael C Ferris at the University of Wisconsin Madison This thesis is concerned with algorithms and software for the solution of the Mixed Complementarity Problem or MCP The MCP formulation is useful for expressing systems of nonlinear inequalities and equations the complementarity al...

This paper describes the development and test in simulation of a coast line following preview controller for the DELFIMx autonomous surface craft (ASC) that takes into account the reference characteristics ahead of the vehicle. The presented solution is based on the definition of an error vector to be driven to zero by the path-following controller. The proposed methodology for controller desig...