Supermodular function: Difference between revisions

Revision as of 21:25, 11 March 2013

Revision as of 20:07, 11 September 2013

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is '''supermodular''' if

:<math>

f(x \loruparrow y) + f(x \landdownarrow y) \geq f(x) + f(y)

</math>

for all ''x'', ''y'' <math>\isin </math> ''R''^''k'', where ''x'' <math>\veeuparrow</math> ''y'' denotes the componentwise maximum and ''x'' <math>\wedgedownarrow</math> ''y'' the componentwise minimum of ''x'' and ''y''.

If &minus;''f'' is supermodular then ''f'' is called '''submodular''', and if the inequality is changed to an equality the function is '''modular'''.