*very* basic i'm sure misunderstanding from combinatorial optimization book

From: ben (ben_at_mailinator.com)
Date: 03/23/05 

Date: 23 Mar 2005 06:37:07 -0800

hello,

i got a new book today -- "combinatorial optimizaiton" by Papadimitriou
and Steiglitz. 3rd sentance of page 1 and i already don't understand
something -- not looking good.

from the book:

Over the past few decades a hierarchy of such problems has emerged
together with a corresponding collection of techniques for their
solution. At one end of this hierarchy is the general nonlinear
programming problem: Find x to

             minimise f(x)
             subject to g_i(x) >= 0 i = 1, . . . , m
                        h_j(x) = 0 j = 1, . . . , p

i don't understand the part after minimise f(x) and haven't tried to
properly yet (maybe i should..) but that isn't what i'm asking about. i
want to get this bit straight first: "minimise f(x)" says to me,
especially as it's in an optimisation book, make the code/operation of
the f() function more efficient -- give the same result, cheaper (that
might be what i've got misunderstood?) but before "minimise f(x)" it
says "find x to". unless the x's in "find x to" and "minimise f(x)" are
representing different things, which i don't think they are, that
really doens't make sense to me -- x is f()'s input and you don't and
can't streamline a function's operations with input into it. so maybe
"minimise f(x)" doesn't mean make the function f() more efficient? can
anyone put me out of my stupidity on this?

thanks, ben.