The Collaborative International Dictionary of English v.0.48:

minimize \min"i*mize\ (m[i^]n"[i^]*m[imac]z), v. t. [imp. & p.
   p. minimized (m[i^]n"[i^]*m[imac]zd); p. pr. & vb. n.
   minimizing (m[i^]n"[i^]*m[imac]*z[i^]ng).]
   1. To reduce to the smallest part or proportion possible; to
      reduce to a minimum. --Bentham.
      [1913 Webster]

   2. To represent, to oneself or others, as of no importance or
      minimal importance or effect; to belittle or disarage.
      [PJC]

WordNet (r) 3.0 (2006):

minimize
    v 1: make small or insignificant; "Let's minimize the risk"
         [syn: minimize, minimise] [ant: maximise, maximize]
    2: represent as less significant or important [syn:
       understate, minimize, minimise, downplay] [ant:
       amplify, exaggerate, hyperbolise, hyperbolize,
       magnify, overdraw, overstate]
    3: cause to seem less serious; play down; "Don't belittle his
       influence" [syn: minimize, belittle, denigrate,
       derogate]