Strong Stationarity Conditions for Optimal Control of Hybrid Systems

We present necessary and sufficient optimality conditions for finite time optimal control problems for a class of hybrid systems described by linear complementarity models. Although these optimal control problems are difficult in general due to the presence of complementarity constraints, we provide a set of structural assumptions ensuring that the tangent cone of the constraints possesses geometric regularity properties. These imply that the classical Karush-Kuhn-Tucker conditions of nonlinear programming theory are both necessary and sufficient for local optimality, which is not the case for general mathematical programs with complementarity constraints. We also present sufficient conditions for global optimality. We proceed to show that the dynamics of every continuous piecewise affine system can be written as the optimizer of a mathematical program which results in a linear complementarity model satisfying our structural assumptions. Hence, our stationarity results apply to a large class of hybrid systems with piecewise affine dynamics. We present simulation results showing the substantial benefits possible from using a nonlinear programming approach to the optimal control problem with complementarity constraints instead of a more traditional mixed-integer formulation.Comment: 30 pages, 4 figure

A semismooth newton method for the nearest Euclidean distance matrix problem

The Nearest Euclidean distance matrix problem (NEDM) is a fundamentalcomputational problem in applications such asmultidimensional scaling and molecularconformation from nuclear magnetic resonance data in computational chemistry.Especially in the latter application, the problem is often large scale with the number ofatoms ranging from a few hundreds to a few thousands.In this paper, we introduce asemismooth Newton method that solves the dual problem of (NEDM). We prove that themethod is quadratically convergent.We then present an application of the Newton method to NEDM with $H$-weights.We demonstrate the superior performance of the Newton method over existing methodsincluding the latest quadratic semi-definite programming solver.This research also opens a new avenue towards efficient solution methods for the molecularembedding problem

The Theoretical Astrophysical Observatory: Cloud-Based Mock Galaxy Catalogues

We introduce the Theoretical Astrophysical Observatory (TAO), an online virtual laboratory that houses mock observations of galaxy survey data. Such mocks have become an integral part of the modern analysis pipeline. However, building them requires an expert knowledge of galaxy modelling and simulation techniques, significant investment in software development, and access to high performance computing. These requirements make it difficult for a small research team or individual to quickly build a mock catalogue suited to their needs. To address this TAO offers access to multiple cosmological simulations and semi-analytic galaxy formation models from an intuitive and clean web interface. Results can be funnelled through science modules and sent to a dedicated supercomputer for further processing and manipulation. These modules include the ability to (1) construct custom observer light-cones from the simulation data cubes; (2) generate the stellar emission from star formation histories, apply dust extinction, and compute absolute and/or apparent magnitudes; and (3) produce mock images of the sky. All of TAO's features can be accessed without any programming requirements. The modular nature of TAO opens it up for further expansion in the future.Comment: 17 pages, 11 figures, 2 tables; accepted for publication in ApJS. The Theoretical Astrophysical Observatory (TAO) is now open to the public at https://tao.asvo.org.au/. New simulations, models and tools will be added as they become available. Contact [email protected] if you have data you would like to make public through TAO. Feedback and suggestions are very welcom