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multiobj_2009_10_21_02

# multiobj_2009_10_21_02 - 9-1 Multiobjective Least-Squares S...

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9 - 1 Multiobjective Least-Squares S. Lall, Stanford 2009.10.21.02 9. Multiobjective Least-Squares Multi-objective least squares Trade-off curves Weighted-sum objectives Example: trade-off curve

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9 - 2 Multiobjective Least-Squares S. Lall, Stanford 2009.10.21.02 Multi-Objective Least Squares in many problems we have two (or more) objectives we want J 1 = bardbl Ax y bardbl 2 small and also J 2 = bardbl Fx g bardbl 2 small usually the objectives are competing we can make one smaller at the expense of making the other larger common example: F = I,g = 0 : we want bardbl Ax y bardbl small, with small x
x (1) x (2) x (3) J 1 J 2 9 - 3 Multiobjective Least-Squares S. Lall, Stanford 2009.10.21.02 trade-off curve shaded area shows ( J 2 ,J 1 ) achieved by some x R n clear area shows ( J 2 ,J 1 ) not achieved by any x R n boundary of region is called optimal trade-off curve corresponding x called Pareto optimal (for the objectives bardbl Ax y bardbl 2 , bardbl Fx g bardbl 2 )

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multiobj_2009_10_21_02 - 9-1 Multiobjective Least-Squares S...

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