Constrained optimization using a conjugate gradient technique, with control applications

Imperial Users onl

International Conference on Continuous Optimization (ICCOPT) 2019 Conference Book

The Sixth International Conference on Continuous Optimization took place on the campus of the Technical University of Berlin, August 3-8, 2019. The ICCOPT is a flagship conference of the Mathematical Optimization Society (MOS), organized every three years. ICCOPT 2019 was hosted by the Weierstrass Institute for Applied Analysis and Stochastics (WIAS) Berlin. It included a Summer School and a Conference with a series of plenary and semi-plenary talks, organized and contributed sessions, and poster sessions. This book comprises the full conference program. It contains, in particular, the scientific program in survey style as well as with all details, and information on the social program, the venue, special meetings, and more

New Directions for Contact Integrators

Contact integrators are a family of geometric numerical schemes which guarantee the conservation of the contact structure. In this work we review the construction of both the variational and Hamiltonian versions of these methods. We illustrate some of the advantages of geometric integration in the dissipative setting by focusing on models inspired by recent studies in celestial mechanics and cosmology.Comment: To appear as Chapter 24 in GSI 2021, Springer LNCS 1282

On the use and development of advanced computational techniques to determine the properties and behaviour of metastable materials

This thesis contains discussions and results pertaining to three distinct pieces of work, all related by an underlying theme: the use and development of computational techniques to discover and characterise novel metastable materials. Zinc oxide is a cheap and abundant material with many potential uses in the electronics and Optics industries. However, its wurtzite ground state structure gives rise to a number of undesirable properties. Thus, knowledge of how to stabilise more useful metastable phases is desirable. To that end, the mechanism of the pressure-induced phase transition between the zincblende and rocksalt polymorphs of the compound was deduced using transition path sampling. Following this, a novel technique combining TPS methods with metadynamics was applied to classify the free-energy landscape relevant to the transition pathway. This provided further information relating to the transition that would have been impossible to determine using path based analyses alone. Water ice exhibits a wealth of structural polymorphism, with at least eighteen phases known to experiment and many more configurations predicted. However, a true understanding of the transition pathways that link these structures remains elusive. Using both metadynamics techniques and a novel procedure known as rotational shooting, attempts to deduce pathways between different phases of ice have been made. The results presented include successful transformations between two crystalline phases of ice and several amorphous phases, as well as the possible elucidation of a novel ice polymorph. Crystal structure prediction remains a challenge in materials science. Using a random structure search technique, eight novel allotropes of carbon and three novel high-pressure polymorphs of zinc oxide have been found and subsequently characterised using density functional theory. Each of the materials displays its own unique array of properties, demonstrating both the variety exhibited by polymorphs of the same material and the ability of random structure prediction techniques to predict such dissimilar materials

Information Geometry

This Special Issue of the journal Entropy, titled “Information Geometry I”, contains a collection of 17 papers concerning the foundations and applications of information geometry. Based on a geometrical interpretation of probability, information geometry has become a rich mathematical field employing the methods of differential geometry. It has numerous applications to data science, physics, and neuroscience. Presenting original research, yet written in an accessible, tutorial style, this collection of papers will be useful for scientists who are new to the field, while providing an excellent reference for the more experienced researcher. Several papers are written by authorities in the field, and topics cover the foundations of information geometry, as well as applications to statistics, Bayesian inference, machine learning, complex systems, physics, and neuroscience

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described