Since I still receive replies to my question to opt-net on quadratic 
programming, I post here a summary of the most relevent information I 
received. (Thanks to Janos Mayer, Richard Cottle, Peter Spellucci, 
Klaus Meer, Jean-Baptiste Hirriart-Urruti, Mike Todd, Florian Jarre,
Diethard Klatte, and Henry Wolkowicz.)


Frank-Wolfe Theorem:
-------------------
Every quadratic program whose objective function is bounded below on 
the feasible set has a finite global minimizer.


This is proved and generalized in the following papers:

Frank, M, Wolfe, P. 
An algorithm for quadratic programming,
Naval Research Logistics Quarterly, 3 (1956) 95-110

Eaves, B.C.
On quadratic programming,
Management Science 17 (1971) 698-711

Keri, G.
On the minimum value of a quadratic function under linear constraints,
Studia Scientiarum Mathematicarum Hungarica  6 (1971) 193-196

Blum, E., Oettli, W.
Direct proof of the existence theorem in quadratic programming, 
Operations Research 20 (1972) 165-167

Perold, A.F. 
A generalization of the Frank-Wolfe theorem,
Mathematical Programming 18 (1980) 215-27.

Zhi-Quan Luo and Shuzhong Zhang, 
On extensions of the Frank-Wolfe theorem,
Computational Optimization and Applications 13 (1999), 87-110. 

E.G. Belousov proved the analogous result for cubic objective functions
(see: Andronov V.G.,Belousov E.G.,Sironin V.M.: O razresimosti 
zadaci polinomial'nogo programmirovanija ,Izvestija Akademii nauk 
SSSR,Techniceskaja kibernetika,1982,Nr.4,pp.194-196)

Diethard Klatte (klatte@ior.unizh.ch) and Florian Jarre 
(jarre@opt.uni-duesseldorf.de) sent me preprints of recent related work.


Arnold Neumaier