solution of quadratic constraint satisfaction problems

Abstract. This paper discusses the problem what makes a computer-assisted proof trustworthy, the quest for an algorithmic support system for computerassisted proof, relations to global optimization, an analysis of some recent proofs, and some current challenges which appear to be amenable to a computerassisted treatment. 1

Abstract. This paper serves as background information for the Vienna proposal for interval standardization, explaining what is needed in practice to make competent use of the interval arithmetic provided by an implementation of the standard to be. Discussed are methods to improve the quality of interval enclosures of the range of a function over a box, considerations of possible hardware support facilitating the implementation of such methods, and the results of a simple interval challenge that I had posed to the reliable computing mailing list on November 26, 2008. Also given is an example of a bound constrained global optimization problem in 4 variables that has a 2-dimensional continuum of global minimizers. This makes standard branch and bound codes extremely slow, and therefore may serve as a useful degenerate test problem.