547,463 research outputs found
Zero-Sum Stochastic Games with Partial Information and Average Payoff
We consider discrete time partially observable zero-sum stochastic game with
average payoff criterion. We study the game using an equivalent completely
observable game. We show that the game has a value and also we come up with a
pair of optimal strategies for both the players.Comment: Journal of Optimization Theory and Applications, 201
On Solving Large-Scale Finite Minimax Problems using Exponential Smoothing
Journal of Optimization Theory and Applications, Vol. 148, No. 2, pp. 390-421
Strong local optimality for generalized L1 optimal control problems
In this paper, we analyse control affine optimal control problems with a cost
functional involving the absolute value of the control. The Pontryagin
extremals associated with such systems are given by (possible) concatenations
of bang arcs with singular arcs and with inactivated arcs, that is, arcs where
the control is identically zero. Here we consider Pontryagin extremals given by
a bang-inactive-bang concatenation. We establish sufficient optimality
conditions for such extremals, in terms of some regularity conditions and of
the coercivity of a suitable finite-dimensional second variation.Comment: Journal of Optimization Theory and Applications, Springer Verlag, In
pres
Necessary Optimality Conditions for Higher-Order Infinite Horizon Variational Problems on Time Scales
We obtain Euler-Lagrange and transversality optimality conditions for
higher-order infinite horizon variational problems on a time scale. The new
necessary optimality conditions improve the classical results both in the
continuous and discrete settings: our results seem new and interesting even in
the particular cases when the time scale is the set of real numbers or the set
of integers.Comment: This is a preprint of a paper whose final and definite form will
appear in Journal of Optimization Theory and Applications (JOTA). Paper
submitted 17-Nov-2011; revised 24-March-2012 and 10-April-2012; accepted for
publication 15-April-201
On the Bail-Out Optimal Dividend Problem
This paper studies the optimal dividend problem with capital injection under
the constraint that the cumulative dividend strategy is absolutely continuous.
We consider an open problem of the general spectrally negative case and derive
the optimal solution explicitly using the fluctuation identities of the
refracted-reflected L\'evy process. The optimal strategy as well as the value
function are concisely written in terms of the scale function. Numerical
results are also provided to confirm the analytical conclusions.Comment: To appear in Journal of Optimization Theory and Applications.
Keywords: stochastic control, scale functions, refracted-reflected L\'evy
processes, bail-out dividend proble
Network Synthesis of Linear Dynamical Quantum Stochastic Systems
The purpose of this paper is to develop a synthesis theory for linear
dynamical quantum stochastic systems that are encountered in linear quantum
optics and in phenomenological models of linear quantum circuits. In
particular, such a theory will enable the systematic realization of
coherent/fully quantum linear stochastic controllers for quantum control,
amongst other potential applications. We show how general linear dynamical
quantum stochastic systems can be constructed by assembling an appropriate
interconnection of one degree of freedom open quantum harmonic oscillators and,
in the quantum optics setting, discuss how such a network of oscillators can be
approximately synthesized or implemented in a systematic way from some linear
and non-linear quantum optical elements. An example is also provided to
illustrate the theory.Comment: Revised and corrected version, published in SIAM Journal on Control
and Optimization, 200
Solving rank-constrained semidefinite programs in exact arithmetic
We consider the problem of minimizing a linear function over an affine
section of the cone of positive semidefinite matrices, with the additional
constraint that the feasible matrix has prescribed rank. When the rank
constraint is active, this is a non-convex optimization problem, otherwise it
is a semidefinite program. Both find numerous applications especially in
systems control theory and combinatorial optimization, but even in more general
contexts such as polynomial optimization or real algebra. While numerical
algorithms exist for solving this problem, such as interior-point or
Newton-like algorithms, in this paper we propose an approach based on symbolic
computation. We design an exact algorithm for solving rank-constrained
semidefinite programs, whose complexity is essentially quadratic on natural
degree bounds associated to the given optimization problem: for subfamilies of
the problem where the size of the feasible matrix is fixed, the complexity is
polynomial in the number of variables. The algorithm works under assumptions on
the input data: we prove that these assumptions are generically satisfied. We
also implement it in Maple and discuss practical experiments.Comment: Published at ISSAC 2016. Extended version submitted to the Journal of
Symbolic Computatio
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