6,371 research outputs found
A note on QUBO instances defined on Chimera graphs
McGeoch and Wang (2013) recently obtained optimal or near-optimal solutions
to some quadratic unconstrained boolean optimization (QUBO) problem instances
using a 439 qubit D-Wave Two quantum computing system in much less time than
with the IBM ILOG CPLEX mixed-integer quadratic programming (MIQP) solver. The
problems studied by McGeoch and Wang are defined on subgraphs -- with up to 439
nodes -- of Chimera graphs. We observe that after a standard reformulation of
the QUBO problem as a mixed-integer linear program (MILP), the specific
instances used by McGeoch and Wang can be solved to optimality with the CPLEX
MILP solver in much less time than the time reported in McGeoch and Wang for
the CPLEX MIQP solver. However, the solution time is still more than the time
taken by the D-Wave computer in the McGeoch-Wang tests.Comment: Version 1 discussed computational results with random QUBO instances.
McGeoch and Wang made an error in describing the instances they used; they
did not use random QUBO instances but rather random Ising Model instances
with fields (mapped to QUBO instances). The current version of the note
reports on tests with the precise instances used by McGeoch and Wan
Fast solution of Cahn-Hilliard variational inequalities using implicit time discretization and finite elements
We consider the e�cient solution of the Cahn-Hilliard variational inequality using an implicit time discretization, which is formulated as an optimal control problem with pointwise constraints on the control. By applying a semi-smooth Newton method combined with a Moreau-Yosida regularization technique for handling the control constraints we show superlinear convergence in function space. At the heart of this method lies the solution of large and sparse linear systems for which we propose the use of preconditioned Krylov subspace solvers using an e�ective Schur complement approximation. Numerical results illustrate the competitiveness of this approach
Joint Antenna Selection and Phase-Only Beamforming Using Mixed-Integer Nonlinear Programming
In this paper, we consider the problem of joint antenna selection and analog
beamformer design in downlink single-group multicast networks. Our objective is
to reduce the hardware costs by minimizing the number of required phase
shifters at the transmitter while fulfilling given distortion limits at the
receivers. We formulate the problem as an L0 minimization problem and devise a
novel branch-and-cut based algorithm to solve the resulting mixed-integer
nonlinear program to optimality. We also propose a suboptimal heuristic
algorithm to solve the above problem approximately with a low computational
complexity. Computational results illustrate that the solutions produced by the
proposed heuristic algorithm are optimal in most cases. The results also
indicate that the performance of the optimal methods can be significantly
improved by initializing with the result of the suboptimal method.Comment: to be presented at WSA 201
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