Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
Results
Showing 1 to 17 of 17 for “"Convex Optimisation."”.
-
Optimisation of Rail-road Level Crossing Closing Time in a Heterogenous Railway Traffic: Towards Safety Improvement - South African Case Study
… influence on the level crossing closing time. Convex optimisation with the objective to minimise the level crossing closing time is formulated taking into account identified features. Moreover, the objective function is constrained by the train's traction characteristics along the constituent …
-
Designing Provably Convergent Algorithms from the Geometry of Data
… can be made to have useful properties such as convexity, non-expansiveness, monotonicity and invertibility. In this dissertation, we develop algorithms in the context of optimisation and sampling, leveraging the expressive strengths of machine learning while maintaining theoretical …
-
Convex Relaxations: Beyond Polynomials, Splitting Methods and Average Case Analysis
… the use of semidefinite programming for solving optimisation problems involving non-polynomial and non-semialgebraic functions. We start with the problem of determining the logarithmic Sobolev constant of a finite Markov chain, which can be framed as a nonconvex optimisation problem involving an …
-
Numerical optimisation methods for power consumption in multi-hop mobile phone networks
… inherent to both mathematical models is nonconvex, therefore we have a non convex optimisation problem. Since the problem is non convex, the obtained solutions are only local minimisers. We present and prove two theorems which, in general terms, state that at a local minimiser, the capacity …
-
Mathematical Challenges in Electron Microscopy
… specific to electron microscopy, developing new optimisation methods for these problems, and modelling new inverse problems to extend the capabilities of existing microscopes. One focus is the application of a directional total variation to overcome the limited angle problem in electron …
-
Calculating thermochemical equilibrium for multiphysics simulations of nuclear materials : development of yellowjacket gibbs energy minimiser
… of thermodynamics to solve a non-linear, non-convex optimisation problem. Several thermodynamic models, including the Modified Quasichemical Model in Quadruplet Approximation (MQMQA) were implemented, and state-of-the art numerical solvers in Portable, Extensible Toolkit for Scientific …
-
Development of a vehicle dynamics controller for obstacle avoidance
… trajectory is obtained using a multi-stage convex optimisation procedure. The overall controller performance is validated by simulation using a complex proprietary model of the vehicle that is reported to have been validated and calibrated against experimental data over several years of use …
-
Verification of advanced controllers for safety-critical systems
… allows us to consider problems like general non-convex optimisation, exact computation of structured singular value, and synthesis of non-convex feasible parameter sets. In practice, the generality of algorithms like quantifier elimination by cylindrical algebraic decomposition come with a …
-
Topics in shape-constrained inference
… above. To this end, we apply techniques from convex geometry and real analysis to elucidate the structural properties of such densities, and obtain some results of independent interest. In the third chapter, we consider the nonparametric estimation of an S-shaped regression function. The least …
-
Local maximum entropy approximation-based modelling of the canine heart
… Galerkin method (EFG). The method is based on a convex optimisation scheme where a non-linear equation is solved with the help of a Newton algorithm, implemented in an in-house code called SESKA. In this study, the aim is to compare LME and MLS and highlight the differences. Preliminary benchmark …
-
Safe online learning for nonlinear dynamical systems using control contraction metrics
… A generic safe learning process is defined and a convex optimisation learning pipeline is developed to handle nonlinear system identification and online controller synthesis via control contraction metrics. The developed pipeline is applied to a longitudinal simulation of an F-16 aircraft using …
-
Optimising energy efficiency and spectral efficiency in multi-tier heterogeneous networks : performance and tradeoffs
… HetNets. The formulated problem is solved using convex optimisation methods to obtain the Pareto-optimal solution for the various network parameters.
-
Robust scheduling control of aeroelasticity.
… Linear Matrix Inequalities (LMIs), which are convex optimisation problems that can be used to represent many linear control objectives. Using LMIs, these LPV controllers can be constructed such that they self-schedule with airspeed and provide upper performance bounds during the design …
-
Vertical axis wind turbine acoustics
… proposed. This inversion method utilised a novel convex optimisation technique that was found to generate good solutions in the simulated test cases, even in the presence of significant random noise. The method was found to be insensitive at low frequencies, which made it ineffective for inverting …
-
Deep Learning Approaches for PDE-based Image Analysis and Beyond: From the Total Variation Flow to Medieval Paper Analysis
… involves solving multiple non-smooth optimisation problems to solve the governing PDE - the TV flow - and is therefore computationally highly intensive. In the first part of the thesis, we present a supervised neural network approximation of the spectral TV decomposition which …
-
Geometric methods in computational optimal transport and high-dimensional inference
… in a single loop procedure for optimising convex functions over transport polytopes. For B-Lipschitz objectives, it is shown that the algorithm achieves an O B√δT regret bound, where δ measures the complexity of the marginal constraints. When applied to optimal transport, this leads to a …
-
Variational Multi-Task Models for Image Analysis: Applications to Magnetic Resonance Imaging
… reconstruction and image segmentation using non-convex Bregman iteration. We describe theoretical and numerical details of the problem and its optimisation scheme. Moreover, we show that our multi-task model achieves better results in several examples and MRI applications than existing approaches …