Thursday, December 14, 2017
'Fundamentals of Optimization'
'1. P1 := {x É›Rn : A(1)x = b(1), x≥0}≠Φ\nP2 := {x É›Rn : A(2)x = b(2), x≥0}≠Φ\nA(1) É›Rm1Xn, A(2) É›Rm2Xn, b(1) É›Rm1 , b(2) É›Rm2.\nP1 x P2 := {(u, v) É›R2n: u É›P1, v É›P2}\nlet x=,\n2. x1 + 2x2 2147383647x3 + x4 = 3\n2x1 x2 +17189128703x3+ 2x4 = 1\nx1, x2, x3, x4 ≥0\na.\nb,\n3. A É›Rmxn, (A) = m and b É›Rm\nF := {xÉ›Rn: Ax=b, x≥0}\nxÉ›Rn is an thoroughgoing principal of F if Ạis a radical executable ascendent of {Ax = b, x≥ 0}\n4. A É›Rmxn (A) = m and b É›Rm\na. {x É›Rn : Ax =b, x≥0}, c É›Rn\n guckimize cTx orbit to Ax = b\nx ≥ 0 is unmeasured\nb. {x É›Rn : Ax =b, x≥0}is numberless and has at to the lowest degree ane natural top\n5. (P) { áº}\n6. F::= (x É›R3 : x λ1e1+ λ2e2+ λ3e3 + ue, for some(a) λ É›R3+, u É› R, e-T λ =1}\nF := Axb { A É›Rmx3, b É›Rm}\n7. max {cT x: Ax = b, x ≥ 0),\nA := 1 2 2 2 2 2 2 7 1\n1 1 1 2 1 1 1 5 2\n1 1 2 1 4 -2 0 , b := 5 , c := 2\n1 2 1 1 -1 4 0 5 2\n6\n4\n-4\nB := {1,2,3,4}, x*B = [1,1,1,1,1]\n8. n>m , A É›Rmxn, (A) =m\n increase cTx belittle bTy\n(P) field to Ax = b and (D) equal to(p) to ATy-s =c\nx ≥0 s ≥ -\n9. (A,b, c) (A É›Rmxn, regulate (A) =m), y É›Rm,\nc := c - ATy\nd É›Rn, Ad =0, c-Td = cTd'
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