31,485 research outputs found
A Distributed Asynchronous Method of Multipliers for Constrained Nonconvex Optimization
This paper presents a fully asynchronous and distributed approach for
tackling optimization problems in which both the objective function and the
constraints may be nonconvex. In the considered network setting each node is
active upon triggering of a local timer and has access only to a portion of the
objective function and to a subset of the constraints. In the proposed
technique, based on the method of multipliers, each node performs, when it
wakes up, either a descent step on a local augmented Lagrangian or an ascent
step on the local multiplier vector. Nodes realize when to switch from the
descent step to the ascent one through an asynchronous distributed logic-AND,
which detects when all the nodes have reached a predefined tolerance in the
minimization of the augmented Lagrangian. It is shown that the resulting
distributed algorithm is equivalent to a block coordinate descent for the
minimization of the global augmented Lagrangian. This allows one to extend the
properties of the centralized method of multipliers to the considered
distributed framework. Two application examples are presented to validate the
proposed approach: a distributed source localization problem and the parameter
estimation of a neural network.Comment: arXiv admin note: substantial text overlap with arXiv:1803.0648
Crossing Minimization for 1-page and 2-page Drawings of Graphs with Bounded Treewidth
We investigate crossing minimization for 1-page and 2-page book drawings. We
show that computing the 1-page crossing number is fixed-parameter tractable
with respect to the number of crossings, that testing 2-page planarity is
fixed-parameter tractable with respect to treewidth, and that computing the
2-page crossing number is fixed-parameter tractable with respect to the sum of
the number of crossings and the treewidth of the input graph. We prove these
results via Courcelle's theorem on the fixed-parameter tractability of
properties expressible in monadic second order logic for graphs of bounded
treewidth.Comment: Graph Drawing 201
Robust Model Predictive Control for Signal Temporal Logic Synthesis
Most automated systems operate in uncertain or adversarial conditions, and have to be capable of reliably reacting to changes in the environment. The focus of this paper is on automatically synthesizing reactive controllers for cyber-physical systems subject to signal temporal logic (STL) specifications. We build on recent work that encodes STL specifications as mixed integer linear constraints on the variables of a discrete-time model of the system and environment dynamics. To obtain a reactive controller, we present solutions to the worst-case model predictive control (MPC) problem using a suite of mixed integer linear programming techniques. We demonstrate the comparative effectiveness of several existing worst-case MPC techniques, when applied to the problem of control subject to temporal logic specifications; our empirical results emphasize the need to develop specialized solutions for this domain
Minimization via duality
We show how to use duality theory to construct minimized versions of a wide class of automata. We work out three cases in detail: (a variant of) ordinary automata, weighted automata and probabilistic automata. The basic idea is that instead of constructing a maximal quotient we go to the dual and look for a minimal subalgebra and then return to the original category. Duality ensures that the minimal subobject becomes the maximally quotiented object
On Bisimulations for Description Logics
We study bisimulations for useful description logics. The simplest among the
considered logics is (a variant of PDL). The others
extend that logic with inverse roles, nominals, quantified number restrictions,
the universal role, and/or the concept constructor for expressing the local
reflexivity of a role. They also allow role axioms. We give results about
invariance of concepts, TBoxes and ABoxes, preservation of RBoxes and knowledge
bases, and the Hennessy-Milner property w.r.t. bisimulations in the considered
description logics. Using the invariance results we compare the expressiveness
of the considered description logics w.r.t. concepts, TBoxes and ABoxes. Our
results about separating the expressiveness of description logics are naturally
extended to the case when instead of we have any sublogic
of that extends . We also provide results
on the largest auto-bisimulations and quotient interpretations w.r.t. such
equivalence relations. Such results are useful for minimizing interpretations
and concept learning in description logics. To deal with minimizing
interpretations for the case when the considered logic allows quantified number
restrictions and/or the constructor for the local reflexivity of a role, we
introduce a new notion called QS-interpretation, which is needed for obtaining
expected results. By adapting Hopcroft's automaton minimization algorithm and
the Paige-Tarjan algorithm, we give efficient algorithms for computing the
partition corresponding to the largest auto-bisimulation of a finite
interpretation.Comment: 42 page
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