Semidefinite Programming Relaxation vs Polyhedral Homotopy ...

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Some essential differences between HomotopyContinuation and (sparse) SDP Relaxation — 2:Workshop on Advances in Optimization, April 19-21, 2007 – p.24/24
Some essential differences between HomotopyContinuation and (sparse) SDP Relaxation — 2:(d) SDPR is sensitive to degrees of polynomials of a POPbecause the SDP relaxed problem becomes larger rapidlyas they increase.⇒ SDPR can be applied to POPs with lower degreepolynomials such as degree ≤ 4 in practice.(e) HC fits parallel computation more than SDPR.(f) The effectiveness of sparse SDPR depends on thec-sparsity; for example, discretization of ODE, DAE,Optimal control problem and PDE.Workshop on Advances in Optimization, April 19-21, 2007 – p.24/24
Page 1 and 2: Semidefinite Programming Relaxation
Page 3 and 4: Contents1. PHoMpara — Parallel im
Page 5 and 6: The polyhedral homotopy methodImple
Page 7 and 8: Numerical results: Hardware — PC
Page 9 and 10: POP min. f 0 (x) s.t. f j (x) ≥ 0
Page 11 and 12: POP min. f 0 (x) s.t. f j (x) ≥ 0
Page 13 and 14: Sparse (SDP) relaxation = Lasserre
Page 17 and 18: A POP alkyl from globalibmin − 6.
Page 19 and 20: Systems of polynomial equationsIs t
Page 21 and 22: Katsura n system of polynomial equa
Page 23 and 24: Katsura n system of polynomial equa
Page 25 and 26: cyclic n system of polynomial equat
Page 27 and 28: Discretization of Mimura’s ODE wi
Page 33 and 34: Discretization of DAE with 3 unknow
Page 35 and 36: 21.81.61.41.210.80.60.40.200 0.2 0.
Page 39: Some essential differences between

Semidefinite Programming Relaxation vs Polyhedral Homotopy ...

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