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41 
A BSpline Geometric Modeling Methodology for Free Surface SimulationNandihalli, Sunil S 08 May 2004 (has links)
Modeling the free surface flows is important in order to estimate the total drag of the sea Vessels. It is also necessary to study the effects of various maritime maneuvers. In this work, different ways of approximating an unstructured free surface grid with a Bspline surface are investigated. The Least squares and Galerkin approaches are studied in this regard. Bspline nite element method (BSPFEM) is studied for the solution of the steadystate kinematic free surface equation. The volume grid has to be moved in order to match the free boundary when the surfacetracking approach is adopted for the solution of free surface problem. Inherent smoothness of the Bspline representation of the free surface aids this process. Bspline representation of the free surface aids in building viscous volume grids hose boundaries closely match the steady state free surface. The Bspline approximation algorithm and BSPFEM solution of free surface equation have been tested with hypothetical algebraic testcases and real cases such as Gbody, Wigley hull and David Taylor Model Basin(DTMB) 5415 hull series.

42 
New insights into conjugate dualityGrad, Sorin  Mihai 13 July 2006 (has links)
With this thesis we bring some new results and improve some
existing ones in conjugate duality and some of the areas it is
applied in.
First we recall the way Lagrange, Fenchel and Fenchel  Lagrange
dual problems to a given primal optimization problem can be
obtained via perturbations and we present some connections between
them. For the Fenchel  Lagrange dual problem we prove strong
duality under more general conditions than known so far, while for
the Fenchel duality we show that the convexity assumptions on the
functions involved can be weakened without altering the
conclusion. In order to prove the latter we prove also that some
formulae concerning conjugate functions given so far only for
convex functions hold also for almost convex, respectively nearly
convex functions.
After proving that the generalized geometric dual problem can be
obtained via perturbations, we show that the geometric duality is
a special case of the Fenchel  Lagrange duality and the strong
duality can be obtained under weaker conditions than stated in the
existing literature. For various problems treated in the
literature via geometric duality we show that Fenchel  Lagrange
duality is easier to apply, bringing moreover strong duality and
optimality conditions under weaker assumptions.
The results presented so far are applied also in convex composite
optimization and entropy optimization. For the composed convex
cone  constrained optimization problem we give strong duality and
the related optimality conditions, then we apply these when
showing that the formula of the conjugate of the precomposition
with a proper convex K  increasing function of a K  convex
function on some n  dimensional non  empty convex set X, where
K is a k  dimensional non  empty closed convex cone, holds under
weaker conditions than known so far. Another field were we apply
these results is vector optimization, where we provide a general
duality framework based on a more general scalarization that
includes as special cases and improves some previous results in
the literature. Concerning entropy optimization, we treat first
via duality a problem having an entropy  like objective function,
from which arise as special cases some problems found in the
literature on entropy optimization. Finally, an application of
entropy optimization into text classification is presented.

43 
Machine Learning Uplink Power Control in Single Input Multiple Output Cellfree NetworksTai, Yiyang January 2020 (has links)
This thesis considers the uplink of cellfree single input multiple output systems, in which the access points employ matchedfilter reception. In this setting, our objectiveis to develop a scalable uplink power control scheme that relies only on largescale channel gain estimates and is robust to changes in the environment. Specifically, we formulate the problem as maxmin and maxproduct signaltointerference ratio optimization tasks, which can be solved by geometric programming. Next, we study the performance of supervised and unsupervised learning approaches employing a feedforward neural network. We find that both approaches perform close to the optimum achieved by geometric programming, while the unsupervised scheme avoids the precomputation of training data that supervised learning would necessitate for every system or environment modification. / Den här avhandlingen tar hänsyn till upplänken till cellfria multipla utgångssystem med en enda ingång, där åtkomstpunkterna använder matchad filtermottagning. I den här inställningen är vårt mål att utveckla ett skalbart styrsystem för upplänkskraft som endast förlitar sig på storskaliga uppskattningar av kanalökningar och är robusta för förändringar i miljön. Specifikt formulerar vi problemet som maxmin och maxprodukt signaltillstörningsförhållande optimeringsuppgifter, som kan lösas genom geometrisk programmering. Därefter studerar vi resultatet av övervakade och okontrollerade inlärningsmetoder som använder ett framåtriktat neuralt nätverk. Vi finner att båda metoderna fungerar nära det optimala som uppnås genom geometrisk programmering, medan det övervakade schemat undviker förberäkningen av träningsdata som övervakat inlärning skulle kräva för varje system eller miljöändring.

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