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Bundle-based pruning in the max-plus curse of dimensionality free method
Abstract : Recently a new class of techniques termed the
max-plus curse of dimensionality-free methods have been de-
veloped to solve nonlinear optimal control problems. In these
methods the discretization in state space is avoided by using a
max-plus basis expansion of the value function. This requires
storing only the coefficients of the basis functions used for
representation. However, the number of basis functions grows
exponentially with respect to the number of time steps of
propagation to the time horizon of the control problem. This
so called “curse of complexity” can be managed by applying a
pruning procedure which selects the subset of basis functions
that contribute most to the approximation of the value function.
The pruning procedures described thus far in the literature rely
on the solution of a sequence of high dimensional optimization
problems which can become computationally expensive.
In this paper we show that if the max-plus basis functions
are linear and the region of interest in state space is convex, the
pruning problem can be efficiently solved by the bundle method.
This approach combining the bundle method and semidefinite
formulations is applied to the quantum gate synthesis problem,
in which the state space is the special unitary group (which
is non-convex). This is based on the observation that the
convexification of the unitary group leads to an exact relaxation.
The results are studied and validated via examples.
https://hal.inria.fr/hal-01099175
Contributor : Stephane Gaubert <>
Submitted on : Wednesday, December 31, 2014 - 5:40:45 PM
Last modification on : Thursday, March 5, 2020 - 6:34:11 PM
Contributor : Stephane Gaubert <>
Submitted on : Wednesday, December 31, 2014 - 5:40:45 PM
Last modification on : Thursday, March 5, 2020 - 6:34:11 PM
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