Von-Neumann Minimax Theorem Von-Neumann Minimax Theorem. 器盟xAy=热盟器xA 证明(cont'd):把它们都转化为标准形式 max t min r m t- xay≤0j=1,,n ×yj r-> ay≥0 i=1,…,m ×xi m =1 Xr 〉.y=1 ×t 台 i=1 x:≥0 i=1,.,m y≥0 i=1,…,n Equality follows directly from strong duality! Von-Neumann Minimax Theorem Von-Neumann Minimax Theorem. max #∈%! min &∈%" �'�� = min &∈%" max #∈%! �'�� 证明(cont’d)：把它们都转化为标准形式 7 min � � − 2 )./ - �,) �) ≥ 0 ∀� = 1, … , � 2 ,./ - �, = 1 �, ≥ 0 ∀� = 1, … , � max � � − 2 ,./ + �,�,) ≤ 0 ∀� = 1, … , � 2 ,./ + �, = 1 �, ≥ 0 ∀� = 1, … , � × � × �) × � × �, Equality follows directly from strong duality!