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Published: 8 October 201

An Interior Point Method for Linear Programming, with n Active Set Flavor

It is now well established that, especially on large linearprogramming problems, the simplex method typically takes upa number of iterations considerably larger than recentinterior-points methods in order to reach a solution.On the other hand, at each iteration, the size of thelinear system of equations solved by the formercan be significantly less than that of the linearsystem solved by the latter.The algorithm proposed in this paper can be thought ofas a compromise between the two extremes: conceptuallyan interior-point method, it ignores, at each iteration,all constraints except those in a small "active set"(in the dual framework). For sake of simplicity, inthis first attempt, an affine scaling algorithm is usedand strong assumptions are made on the problem. Globaland local quadratic convergence is proved

A lattice in more than two Kac--Moody groups is arithmetic

Let $\Gamma$ be an irreducible lattice in a product of n infinite irreducible complete Kac-Moody groups of simply laced type over finite fields. We show that if n is at least 3, then each Kac-Moody groups is in fact a simple algebraic group over a local field and $\Gamma$ is an arithmetic lattice. This relies on the following alternative which is satisfied by any irreducible lattice provided n is at least 2: either $\Gamma$ is an S-arithmetic (hence linear) group, or it is not residually finite. In that case, it is even virtually simple when the ground field is large enough. More general CAT(0) groups are also considered throughout.Comment: Subsection 2.B was modified and an example was added ther

CONSOLE: A CAD tandem for optimization-based design interacting with user-supplied simulators

CONSOLE employs a recently developed design methodology (International Journal of Control 43:1693-1721) which provides the designer with a congenial environment to express his problem as a multiple ojective constrained optimization problem and allows him to refine his characterization of optimality when a suboptimal design is approached. To this end, in CONSOLE, the designed formulates the design problem using a high-level language and performs design task and explores tradeoff through a few short and clearly defined commands. The range of problems that can be solved efficiently using a CAD tools depends very much on the ability of this tool to be interfaced with user-supplied simulators. For instance, when designing a control system one makes use of the characteristics of the plant, and therefore, a model of the plant under study has to be made available to the CAD tool. CONSOLE allows for an easy interfacing of almost any simulator the user has available. To date CONSOLE has already been used successfully in many applications, including the design of controllers for a flexible arm and for a robotic manipulator and the solution of a parameter selection problem for a neural network

Joint Scheduling and Routing for Ad-hoc Networks Under Channel State Uncertainty

We determine a joint link activation and routing policy that maximizes the stable throughput region of time-varying wireless ad-hoc networks with multiple commodities. In practice, the state of the channel process from the time it is observed till the time a transmission actually takes place can be significantly different. With this in mind, we introduce a stationary policy that takes scheduling and routing decisions based on a possibly inaccurate estimate of the true channel state. We show optimality of this policy within a broad class of link activation processes. In particular, processes in this class may be induced by any policy, possibly non-stationary, even anticipative and aware of the entire sample paths, including the future, of the arrival, estimated and true channel state processes, as long as it has no knowledge on the current true channel state, besides that available through the estimated channel state

Unified N=2 Maxwell-Einstein and Yang-Mills-Einstein Supergravity Theories in Four Dimensions

We study unified N=2 Maxwell-Einstein supergravity theories (MESGTs) and unified Yang-Mills Einstein supergravity theories (YMESGTs) in four dimensions. As their defining property, these theories admit the action of a global or local symmetry group that is (i) simple, and (ii) acts irreducibly on all the vector fields of the theory, including the ``graviphoton''. Restricting ourselves to the theories that originate from five dimensions via dimensional reduction, we find that the generic Jordan family of MESGTs with the scalar manifolds [SU(1,1)/U(1)] X [SO(2,n)/SO(2)X SO(n)] are all unified in four dimensions with the unifying global symmetry group SO(2,n). Of these theories only one can be gauged so as to obtain a unified YMESGT with the gauge group SO(2,1). Three of the four magical supergravity theories defined by simple Euclidean Jordan algebras of degree 3 are unified MESGTs in four dimensions. Two of these can furthermore be gauged so as to obtain 4D unified YMESGTs with gauge groups SO(3,2) and SO(6,2), respectively. The generic non-Jordan family and the theories whose scalar manifolds are homogeneous but not symmetric do not lead to unified MESGTs in four dimensions. The three infinite families of unified five-dimensional MESGTs defined by simple Lorentzian Jordan algebras, whose scalar manifolds are non-homogeneous, do not lead directly to unified MESGTs in four dimensions under dimensional reduction. However, since their manifolds are non-homogeneous we are not able to completely rule out the existence of symplectic sections in which these theories become unified in four dimensions.Comment: 47 pages; latex fil