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In this book we aim to present, in a unified framework, a broad spectrum of mathematical theory that has grown in connection with the study of problems of optimization, equilibrium, control, and stability of linear and nonlinear systems. The title Variational Analysis reflects this breadth. For a long time, ‘variational ’ problems have been identified mostly with the ‘calculus of variations’. In that venerable subject, built around the minimization of integral functionals, constraints were relatively simple and much of the focus was on infinite-dimensional function spaces. A major theme was the exploration of variations around a point, within the bounds imposed by the constraints, in order to help characterize solutions and portray them in terms of ‘variational principles’. Notions of perturbation, approximation and even generalized differentiability were extensively investigated. Variational theory progressed also to the study of so-called stationary points, critical points, and other indications of singularity that a point might have relative to its neighbors, especially in association with existence theorems for differential equations.

This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning, planning under uncertainty, sensor-based planning, visibility, decision-theoretic planning, game theory, information spaces, reinforcement learning, nonlinear systems, trajectory planning, nonholonomic planning, and kinodynamic planning.

Performance modelling is concerned with the capture and analysis of the dynamic behaviour of computer and communication systems. The size and complexity of many modern systems result in large, complex models. A compositional approach decomposes the system into subsystems that are smaller and more easily modelled. In this thesis a novel compositional approach to performance modelling is presented. This approach is based on a suitably enhanced process algebra, PEPA (Performance Evaluation Process Algebra). The compositional nature of the language provides benefits for model solution as well as model construction. An operational semantics is provided for PEPA and its use to generate an underlying Markov process for any PEPA model is explained and demonstrated. Model simplification and state space aggregation have been proposed as means to tackle the problems of large performance models. These techniques are presented in terms of notions of equivalence between modelling entities. A framewo...

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In this paper we study both market risks and non-market risks, without complete markets assumption, and discuss methods of measurement of these risks. We present and justify a set of four desirable properties for measures of risk, and call the measures satisfying these properties "coherent". We examine the measures of risk provided and the related actions required by SPAN, by the SEC/NASD rules and by quantile based methods. We demonstrate the universality of scenario-based methods for providing coherent measures. We offer suggestions concerning the SEC method. We also suggest a method to repair the failure of subadditivity of quantile-based methods.

This paper describes an extension to the set of Basic Linear Algebra Subprograms. The extensions are targeted at matrix-vector operations which should provide for efficient and portable implementations of algorithms for high performance computers.

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This paper summarizes the empirical and theoretical research on executive compensation and provides a comprehensive and up-to-date description of pay practices (and trends in pay practices) for chief executive officers (CEOs). Topics discussed include the level and structure of CEO pay (including detailed analyses of annual bonus plans, executive stock options, and option valuation), international pay differences, the pay-setting process, the relation between CEO pay and firm performance (“pay-performance sensitivities”), the relation between sensitivities and subsequent firm performance, relative performance evaluation, executive turnover, and the politics of CEO pay.