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 B-spline surface are investigated. The Least squares and Galerkin approaches are studied in this regard. B-spline nite element method (BSPFEM) is studied for the solution of the steady-state kinematic free surface equation. The volume grid has to be moved in order to match the free boundary when the surface-tracking approach is adopted for the solution of free surface problem. Inherent smoothness of the B-spline representation of the free surface aids this process. B-spline representation of the free surface aids in building viscous volume grids hose boundaries closely match the steady state free surface. The B-spline 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.

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.

This thesis considers the uplink of cell-free single input multiple output systems, in which the access points employ matched-filter reception. In this setting, our objectiveis to develop a scalable uplink power control scheme that relies only on large-scale channel gain estimates and is robust to changes in the environment. Specifically, we formulate the problem as max-min and max-product signal-to-interference ratio optimization tasks, which can be solved by geometric programming. Next, we study the performance of supervised and unsupervised learning approaches employing a feed-forward neural network. We find that both approaches perform close to the optimum achieved by geometric programming, while the unsupervised scheme avoids the pre-computation 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 max-produkt signal-till-störningsförhållande 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.