1,859 research outputs found
Optional Decomposition and Lagrange Multipliers
Let Q be the set of equivalent martingale measures for a given process S, and let X be a process which is a local supermartingale with respect to any measure in Q. The optional decomposition theorem for X states that there exists a predictable integrand ф such that the difference X−ф•S is a decreasing process. In this paper we give a new proof which uses techniques from stochastic calculus rather than functional analysis, and which removes any boundedness assumption
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Revisiting lagrange relaxation (LR) for processing large-scale mixed integer programming (MIP) problems
Lagrangean Relaxation has been successfully applied to process many well known
instances of NP-hard Mixed Integer Programming problems. In this paper we present
a Lagrangean Relaxation based generic solver for processing Mixed Integer
Programming problems. We choose the constraints, which are relaxed using a
constraint classification scheme. The tactical issue of updating the Lagrange
multiplier is addressed through sub-gradient optimisation; alternative rules for
updating their values are investigated. The Lagrangean relaxation provides a lower
bound to the original problem and the upper bound is calculated using a heuristic
technique. The bounds obtained by the Lagrangean Relaxation based generic solver
were used to warm-start the Branch and Bound algorithm; the performance of the
generic solver and the effect of the alternative control settings are reported for a wide
class of benchmark models. Finally, we present an alternative technique to calculate
the upper bound, using a genetic algorithm that benefits from the mathematical
structure of the constraints. The performance of the genetic algorithm is also
presented
Unified and Distributed QoS-Driven Cell Association Algorithms in Heterogeneous Networks
This paper addresses the cell association problem in the downlink of a
multi-tier heterogeneous network (HetNet), where base stations (BSs) have
finite number of resource blocks (RBs) available to distribute among their
associated users. Two problems are defined and treated in this paper: sum
utility of long term rate maximization with long term rate quality of service
(QoS) constraints, and global outage probability minimization with outage QoS
constraints. The first problem is well-suited for low mobility environments,
while the second problem provides a framework to deal with environments with
fast fading. The defined optimization problems in this paper are solved in two
phases: cell association phase followed by the optional RB distribution phase.
We show that the cell association phase of both problems have the same
structure. Based on this similarity, we propose a unified distributed algorithm
with low levels of message passing to for the cell association phase. This
distributed algorithm is derived by relaxing the association constraints and
using Lagrange dual decomposition method. In the RB distribution phase, the
remaining RBs after the cell association phase are distributed among the users.
Simulation results show the superiority of our distributed cell association
scheme compared to schemes that are based on maximum signal to interference
plus noise ratio (SINR)
Generalized Kuhn-Tucker Conditions for N-Firm Stochastic Irreversible Investment under Limited Resources
In this paper we study a continuous time, optimal stochastic investment
problem under limited resources in a market with N firms. The investment
processes are subject to a time-dependent stochastic constraint. Rather than
using a dynamic programming approach, we exploit the concavity of the profit
functional to derive some necessary and sufficient first order conditions for
the corresponding Social Planner optimal policy. Our conditions are a
stochastic infinite-dimensional generalization of the Kuhn-Tucker Theorem. The
Lagrange multiplier takes the form of a nonnegative optional random measure on
[0,T] which is flat off the set of times for which the constraint is binding,
i.e. when all the fuel is spent. As a subproduct we obtain an enlightening
interpretation of the first order conditions for a single firm in Bank (2005).
In the infinite-horizon case, with operating profit functions of Cobb-Douglas
type, our method allows the explicit calculation of the optimal policy in terms
of the `base capacity' process, i.e. the unique solution of the Bank and El
Karoui representation problem (2004).Comment: 25 page
Automated dynamic analytical model improvement for damped structures
A method is described to improve a linear nonproportionally damped analytical model of a structure. The procedure finds the smallest changes in the analytical model such that the improved model matches the measured modal parameters. Features of the method are: (1) ability to properly treat complex valued modal parameters of a damped system; (2) applicability to realistically large structural models; and (3) computationally efficiency without involving eigensolutions and inversion of a large matrix
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