220,474 research outputs found
The Power of Linear Programming for Valued CSPs
A class of valued constraint satisfaction problems (VCSPs) is characterised
by a valued constraint language, a fixed set of cost functions on a finite
domain. An instance of the problem is specified by a sum of cost functions from
the language with the goal to minimise the sum. This framework includes and
generalises well-studied constraint satisfaction problems (CSPs) and maximum
constraint satisfaction problems (Max-CSPs).
Our main result is a precise algebraic characterisation of valued constraint
languages whose instances can be solved exactly by the basic linear programming
relaxation. Using this result, we obtain tractability of several novel and
previously widely-open classes of VCSPs, including problems over valued
constraint languages that are: (1) submodular on arbitrary lattices; (2)
bisubmodular (also known as k-submodular) on arbitrary finite domains; (3)
weakly (and hence strongly) tree-submodular on arbitrary trees.Comment: Corrected a few typo
Choco: an Open Source Java Constraint Programming Library
International audienceChoco is a java library for constraint satisfaction problems (CSP), constraint programming (CP) and explanation-based constraint solving (e-CP). It is built on a event-based propagation mechanism with backtrackable structures
Weak Dynamic Programming for Generalized State Constraints
We provide a dynamic programming principle for stochastic optimal control
problems with expectation constraints. A weak formulation, using test functions
and a probabilistic relaxation of the constraint, avoids restrictions related
to a measurable selection but still implies the Hamilton-Jacobi-Bellman
equation in the viscosity sense. We treat open state constraints as a special
case of expectation constraints and prove a comparison theorem to obtain the
equation for closed state constraints.Comment: 36 pages;forthcoming in 'SIAM Journal on Control and Optimization
On properties of Karlsson Hadamards and sets of Mutually Unbiased Bases in dimension six
The complete classification of all 6x6 complex Hadamard matrices is an open
problem. The 3-parameter Karlsson family encapsulates all Hadamards that have
been parametrised explicitly. We prove that such matrices satisfy a non-trivial
constraint conjectured to hold for (almost) all 6x6 Hadamard matrices. Our
result imposes additional conditions in the linear programming approach to the
mutually unbiased bases problem recently proposed by Matolcsi et al.
Unfortunately running the linear programs we were unable to conclude that a
complete set of mutually unbiased bases cannot be constructed from Karlsson
Hadamards alone.Comment: As published versio
Stochastic Optimal Control, International Finance and Debt
We use stochastic optimal control-dynamic programming (DP) to derive the optimal foreign debt/net worth, consumption/net worth, current account/net worth, and endogenous growth rate in an open economy. Unlike the literature that uses an Intertemporal Budget Constraint (IBC) or the Maximum Principle, the DP approach does not require perfect foresight or certainty equivalence. Errors of measurement and the effects of unanticipated shocks are corrected in an optimal manner. We contrast the DP and IBC approaches, show how the results of the dynamic programming approach can be interpreted in a traditional simple mean-variance/Tobin-Markowitz context, and explain why our results are generalizations of the Merton model.stochastic optimal control, foreign debt, international finance, vulnerability to external shocks, sustainable current account deficits
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