Workshop/Miniconference on Functional Analysis/Optimization

Preface

This volume of the Proceedings of the Centre for Mathematical Analysis contains papers by participants in the Workshop/Miniconference on Functional Analysis/Optimization held in Canberra in August, 1988. Some of the papers were prepared beforehand and were presented at the Miniconference. But importantly, some have resulted from collaboration which occurred there in response to problems raised in the sessions; this is the special return from the prolonged Workshop experience.

The theme of the Workshop/Miniconference was Functional Analysis/Optimization and although most participants worked in one or other of the two areas, a small group worked in both. The pervasive influence of Rockafellar and Clarke meant that in many cases we all had some familiarity with the tools used by each other so there was more unity than might have been expected. Although the papers in this volume are easily identified as being in one of the two areas, a commonality of background is often evident.

We wish to thank the Centre for Mathematical Analysis for making all its facilites available for the August period and for processing these proceedings for publication. In particular we would like to thank the Director, Professor Neil Trudinger for suggesting the conference and for facilitating the visits of our overseas participants. The Workshop/Miniconference attracted participants from Bulgaria, Canada, England, France, Greece, Israel and the United States of America as well as members from ten Australasian universities.

Especially we wish to thank Mrs Marilyn Gray the Secretary of the Centre, who so efficiently handled the administration of the Workshop/Miniconference from early in 1987 when visitor arrangements were being made, up to the end of 1988 when the proceedings were being put to press.

We also thank Mrs Jan Garnsey, secretary to the Department of Mathematics at the University of Newcastle for her assistance with correspondence and Mrs Dorothy Nash for her support during the August meeting.

And, of course, our thanks to our colleagues who made August 1988 in Canberra such a pleasant and productive time.

Simon Fitzpatrick and John Giles
(Editors)

Contents

Chapter Page number
1 - On the connectedness properties of suns in finite dimensional spaces (pdf 1.12 MB)
A.L. Brown
1
2 - An approximation theoretic characterisation of inner product spaces (pdf 668.22 KB)
A.L. Brown
16
3 - Langrangian conditions for a minimax (pdf 1.29 MB)
B.D. Craven
24
4 - Differentiability of distance functions in normed linear spaces with uniformly Gâteaux differentiable norm (pdf 359.33 KB)
Brett Davis
34
5 - On generic differentiability of locally Lipschitz functions on Banach space (pdf 1.06 MB)
G. de Barra, Simon Fitzpatrick and J.R. Giles
39
6 - Contractive projections on Banach spaces (pdf 829.91 KB)
Ian Doust
50
7 - Representing monotone operators by convex functions (pdf 893.46 KB)
Simon Fitzpatrick
59
8 - Nearest points in convex sets in normed linear spaces (pdf 908.43 KB)
Simon Fitzpatrick and John Giles
66
9 - Most of the two-person zero-sum games have unique solution (pdf 1.25 MB)
P.S. Kenderov and N.K. Ribarska
73
10 - Strong density of finite rank operators in subalgebras of B(X) (pdf 1.38 MB)
M.S. Lambrou
83
11 - The convergence of entropic estimates for moment problems (pdf 932.83 KB)
A.S. Lewis
100
12 - Absolutely Chebyshev subspaces (pdf 1.54 MB)
Åsvald Lima and David Yost
116
13 - Non-reflexive realizations of non-distributive subspace lattices (pdf 737.04 KB)
W.E. Longstaff
128
14 - Spaces of large dimension; some counter-intuitive results (pdf 1.01 MB)
V.D. Milman
141
15 - A non-commutative joint spectral theory (pdf 745.12 KB)
A.J. Pryde
153
16 - Invexity in nonlinear programs and control problems (pdf 971.51 KB)
I. Smart
162
17 - Orthogonality and fixed points of nonexpansive maps (pdf 721.88 KB)
Brailey Sims
178
18 - Bellman's equation and a continuous linear programming problem (pdf 1.17 MB)
W.R.S. Sutherland
187
19 - On the differentiability of convex functions (pdf 551.76 KB)
Maria Elena Verona
195
20 - A problem on nearest points in Banach spaces (pdf 235.2 KB)
Jonathon M. Borwein and Simon Fitzpatrick
203
21 - The valuation of contingent securities (pdf 285.34 KB)
A. Brace, A. Lewis and G.N. Newsam
205
22 - Superamenability (pdf 269.71 KB)
R.J. Loy
207