28,530 research outputs found
Light reflection is nonlinear optimization
In this paper, we show that the near field reflector problem is a nonlinear
optimization problem. From the corresponding functional and constraint
function, we derive the Monge-Amp\`ere type equation for such a problem.Comment: to appear in Calc. Var. and PDE
Formal Proofs for Nonlinear Optimization
We present a formally verified global optimization framework. Given a
semialgebraic or transcendental function and a compact semialgebraic domain
, we use the nonlinear maxplus template approximation algorithm to provide a
certified lower bound of over . This method allows to bound in a modular
way some of the constituents of by suprema of quadratic forms with a well
chosen curvature. Thus, we reduce the initial goal to a hierarchy of
semialgebraic optimization problems, solved by sums of squares relaxations. Our
implementation tool interleaves semialgebraic approximations with sums of
squares witnesses to form certificates. It is interfaced with Coq and thus
benefits from the trusted arithmetic available inside the proof assistant. This
feature is used to produce, from the certificates, both valid underestimators
and lower bounds for each approximated constituent. The application range for
such a tool is widespread; for instance Hales' proof of Kepler's conjecture
yields thousands of multivariate transcendental inequalities. We illustrate the
performance of our formal framework on some of these inequalities as well as on
examples from the global optimization literature.Comment: 24 pages, 2 figures, 3 table
Radio Interferometric Calibration Using a Riemannian Manifold
In order to cope with the increased data volumes generated by modern radio
interferometers such as LOFAR (Low Frequency Array) or SKA (Square Kilometre
Array), fast and efficient calibration algorithms are essential. Traditional
radio interferometric calibration is performed using nonlinear optimization
techniques such as the Levenberg-Marquardt algorithm in Euclidean space. In
this paper, we reformulate radio interferometric calibration as a nonlinear
optimization problem on a Riemannian manifold. The reformulated calibration
problem is solved using the Riemannian trust-region method. We show that
calibration on a Riemannian manifold has faster convergence with reduced
computational cost compared to conventional calibration in Euclidean space.Comment: Draft version. Final version will appear in IEEE ICASSP 2013,
http://www.icassp2013.com
Study of non-linear optimization techniques
Nonlinear optimization techniques in dynamic programming and solution of ordinary nonlinear differential equations by Runge-Kutta metho
Optimizing Memory-Bounded Controllers for Decentralized POMDPs
We present a memory-bounded optimization approach for solving
infinite-horizon decentralized POMDPs. Policies for each agent are represented
by stochastic finite state controllers. We formulate the problem of optimizing
these policies as a nonlinear program, leveraging powerful existing nonlinear
optimization techniques for solving the problem. While existing solvers only
guarantee locally optimal solutions, we show that our formulation produces
higher quality controllers than the state-of-the-art approach. We also
incorporate a shared source of randomness in the form of a correlation device
to further increase solution quality with only a limited increase in space and
time. Our experimental results show that nonlinear optimization can be used to
provide high quality, concise solutions to decentralized decision problems
under uncertainty.Comment: Appears in Proceedings of the Twenty-Third Conference on Uncertainty
in Artificial Intelligence (UAI2007
Guest Editorial: Nonlinear Optimization of Communication Systems
Linear programming and other classical optimization techniques have found important applications in communication systems for many decades. Recently, there has been a surge in research activities that utilize the latest developments in nonlinear optimization to tackle a much wider scope of work in the analysis and design of communication systems. These activities involve every “layer” of the protocol stack and the principles of layered network architecture itself, and have made intellectual and practical impacts significantly beyond the established frameworks of optimization of communication systems in the early 1990s. These recent results are driven by new demands in the areas of communications and networking, as well as new tools emerging from optimization theory. Such tools include the powerful theories and highly efficient computational algorithms for nonlinear convex optimization, together with global solution methods and relaxation techniques for nonconvex optimization
Transmission Network Reduction Method using Nonlinear Optimization
This paper presents a new method to determine the susceptances of a reduced
transmission network representation by using nonlinear optimization. We use
Power Transfer Distribution Factors (PTDFs) to convert the original grid into a
reduced version, from which we determine the susceptances. From our case
studies we find that considering a reduced injection-independent evaluated PTDF
matrix is the best approximation and is by far better than an
injection-dependent evaluated PTDF matrix over a given set of
arbitrarily-chosen power injection scenarios. We also compare our nonlinear
approach with existing methods from literature in terms of the approximation
error and computation time. On average, we find that our approach reduces the
mean error of the power flow deviations between the original power system and
its reduced version, while achieving higher but reasonable computation times
Nonlinear Optimization over a Weighted Independence System
We consider the problem of optimizing a nonlinear objective function over a
weighted independence system presented by a linear-optimization oracle. We
provide a polynomial-time algorithm that determines an r-best solution for
nonlinear functions of the total weight of an independent set, where r is a
constant that depends on certain Frobenius numbers of the individual weights
and is independent of the size of the ground set. In contrast, we show that
finding an optimal (0-best) solution requires exponential time even in a very
special case of the problem
- …