Integer Program Optimization: Solving Relaxations - Edubirdie

University:
Massachusetts Institute of Technology
Course:
15.501/516 | Accounting
Academic year:

2023
Views:

177

Pages:

1
Author:

Gunner Petersen

1 Maple Slide 1 • Command: gbasis(W L, T ); – W L list of polynomials – T term order table or short term order description • Example: – with(Groebner) : – W L := [x2 − 2 ∗ x ∗ z + 5, x ∗ y 2 + y ∗ z 3 , 3 ∗ y 2 − 8 ∗ z 3 ] : – gbasis(W L, plex(y, x, z)); – gbasis(W L, tdeg(x, y, z)); 2 Exercise 7.11 Slide 2 Deﬁne: ⎛ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ x3 x2 x y2 y 1 ⎞� ⎛ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ p11 p12 p13 p14 p15 p16 p12 p22 p23 p24 p25 p26 p13 p23 p33 p34 p35 p36 p14 p24 p34 p44 p45 p46 p15 p25 p35 p45 p55 p56 p16 p26 p36 p46 p56 p66 ⎞⎛ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎠⎝ x3 x2 x y2 y 1 ⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ = f (x, y) − γ = 4x2 − 3 21 4 x 10 + 31 x6 + xy − 4y 2 + 4y 4 − γ SDP Formulation Slide 3 min P s.t. p66 P �0 x6 : p11 = 31 x4 : p22 + 2p13 = − 21 10 x2 : p33 + 2p26 = 4 xy : 2p35 = 1 y 2 : p55 + 2p46 = −4 y 4 : p44 = 4 pij = 0 1 for all other i, j

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