10,892 research outputs found
A Finite-Time Cutting Plane Algorithm for Distributed Mixed Integer Linear Programming
Many problems of interest for cyber-physical network systems can be
formulated as Mixed Integer Linear Programs in which the constraints are
distributed among the agents. In this paper we propose a distributed algorithm
to solve this class of optimization problems in a peer-to-peer network with no
coordinator and with limited computation and communication capabilities. In the
proposed algorithm, at each communication round, agents solve locally a small
LP, generate suitable cutting planes, namely intersection cuts and cost-based
cuts, and communicate a fixed number of active constraints, i.e., a candidate
optimal basis. We prove that, if the cost is integer, the algorithm converges
to the lexicographically minimal optimal solution in a finite number of
communication rounds. Finally, through numerical computations, we analyze the
algorithm convergence as a function of the network size.Comment: 6 pages, 3 figure
New observables in topological instantonic field theories
Instantonic theories are quantum field theories where all correlators are
determined by integrals over the finite-dimensional space (space of generalized
instantons). We consider novel geometrical observables in instantonic
topological quantum mechanics that are strikingly different from standard
evaluation observables. These observables allow jumps of special type of the
trajectory (at the point of insertion of such observables).
They do not (anti)commute with evaluation observables and raise the dimension
of the space of allowed configurations, while the evaluation observables lower
this dimension. We study these observables in geometric and operator
formalisms. Simple examples are explicitly computed; they depend on linking of
the points.
The new "arbitrary jump" observables may be used to construct correlation
functions computing e.g. the linking numbers of cycles, as we illustrate on
Hopf fibration.Comment: 16 pages, accepted to Journal of Geometry and Physic
On the relationship between standard intersection cuts, lift-and-project cuts, and generalized intersection cuts
We examine the connections between the classes of cuts in the title. We show that lift-and-project (L&P) cuts from a given disjunction are equivalent to generalized intersection cuts from the family of polyhedra obtained by taking positive combinations of the complements of the inequalities of each term of the disjunction. While L&P cuts from split disjunctions are known to be equivalent to standard intersection cuts (SICs) from the strip obtained by complementing the terms of the split, we show that L&P cuts from more general disjunctions may not be equivalent to any SIC. In particular, we give easily verifiable necessary and sufficient conditions for a L&P cut from a given disjunction D to be equivalent to a SIC from the polyhedral counterpart of D. Irregular L&P cuts, i.e. those that violate these conditions, have interesting properties. For instance, unlike the regular ones, they may cut off part of the corner polyhedron associated with the LP solution from which they are derived. Furthermore, they are not exceptional: their frequency exceeds that of regular cuts. A numerical example illustrates some of the above properties. © 2016 Springer-Verlag Berlin Heidelberg and Mathematical Optimization Societ
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