Synopses & Reviews
This is the first in a new series of contributed, refereed volumes devoted to research in optimization by Australasian researchers and their collaborators. These volumes are intended to have wide scope and include survey papers by established researchers providing up-to-date information on research directions. This volume contains survey papers on the Clarke subdifferential and differentiability in Banach spaces, algorithms for solving nonsmooth equations, and control parametrization schemes in optimal control. Other topics covered include convex optimization, generalized convexity in optimization, nonsmooth analysis, and algorithms using approximations of sub-differentials. Audience: Practitioners, postgraduate students and researchers in optimization.
Synopsis
Although the monograph Progress in Optimization I: Contributions from Aus tralasia grew from the idea of publishing a proceedings of the Fourth Optimiza tion Day, held in July 1997 at the Royal Melbourne Institute of Technology, the focus soon changed to a refereed volume in optimization. The intention is to publish a similar book annually, following each Optimization Day. The idea of having an annual Optimization Day was conceived by Barney Glover; the first of these Optimization Days was held in 1994 at the University of Ballarat. Barney hoped that such a yearly event would bring together the many, but widely dispersed, researchers in Australia who were publishing in optimization and related areas such as control. The first Optimization Day event was followed by similar conferences at The University of New South Wales (1995), The University of Melbourne (1996), the Royal Melbourne Institute of Technology (1997), and The University of Western Australia (1998). The 1999 conference will return to Ballarat University, being organized by Barney's long-time collaborator Alex Rubinov. In recent years the Optimization Day has been held in conjunction with other locally-held national or international conferences. This has widened the scope of the monograph with contributions not only coming from researchers in Australia and neighboring regions but also from their collaborators in Europe and North America."
Table of Contents
List of Figures. List of Tables. Preface. Editors. Part I: Non-Smooth Analysis. 1. A survey of Clarke's subdifferential and the differentiability of locally Lipschitz functions; J.R. Giles. 2. Continuous approximation of nonsmooth mappings; A.M. Rubinov, A. Zaffaroni. Part II: Generalized Convexity. 3. Generalised convexity properties of marginal functions; M. Andramonov, A. Ellero. 4. Fractional programming with invexity; B.D. Craven, B. Mond. 5. Supremal generators of spaces of homogeneous functions; A.M. Rubinov. 6. Higher order convexity and duality in multiobjective programming problems; J. Zhang. Part III: Algorithms for Nonsmooth Programming. 7. A survey of some nonsmooth equations and smoothing Newton methods; L. Qi, D. Sun. 8. Minimization methods for one class of nonsmooth functions and calculation of semi-equilibrium prices; A.M. Bagirov. 9. Potential reduction methods for the nonlinear complementarity problem; H. Jiang. 10. Approximations to the Clarke generalized Jacobians and nonsmooth least-squares minimization; H. Xu, et al. Part IV: Global Optimization. 11. A parametric approach to global optimization problems of a special kind; M. Andramonov. 12. A Concave composite programming perspective on DC programming; L. Churilov, M. Sniedovich. Part V: Control Methodologies. 13. A survey of the control parametrization and control parametrization enhancing methods for constrained optimal control problems; V. Rehbock, et al. 14. Multivariable controllers with time-domain inequality constraints; J.K. Vethecan, R.D. Hill.