Solutions in Cones

Abstract

As a rule, the ‘user’ of mathematical models for problems in science wants to see some additional conditions satisfied before he is willing to call what you have found by purely mathematical reasoning a solution. In many cases nonnegativity is such a minimal requirement. Think for example of concentrations in biological or chemical problems, or of problems where the ‘laws of nature’ prescribe definite lower bounds for the unknowns, so that a fixed shift makes the latter nonnegative.

Words be redundant? And where would one place what stands between the words?

Stanislaw Jerzy Lec

Geometry may sometimes appear to take the lead over analysis, but in fact precedes it only as a servant goes before his master to clear the path and light him on the way.

James Joseph Sylvester