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Lect05

# Lect05 - D Bertsekas EE553 LECTURE 5 LECTURE OUTLINE...

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EE553 LECTURE 5 LECTURE OUTLINE Approaches for Rate of Convergence Analysis The Local Analysis Method Quadratic Model Analysis The Role of the Condition Number Scaling Extension to Nonquadratic Problems Singular and Difﬁcult Problems D. Bertsekas Adapted for USC EE553 by M. Safonov © D. Bertsekas, MIT, Cambridge, MA

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APPROACHES FOR RATE OF CONVERGENCE ANALYSIS Computational complexity approach Informational complexity approach Local analysis Why we will focus on the local analysis method Adapted for USC EE553 by M. Safonov © D. Bertsekas, MIT, Cambridge, MA
THE LOCAL ANALYSIS APPROACH Restrict attention to sequences x k converging to a local min x * Measure progress in terms of an error function e ( x ) 0 with e ( x * ) = 0 , such as e ( x ) = k x - x * k , e ( x ) = | f ( x ) - f ( x * ) | Compare the tail of the sequence e ( x k ) with the tail of standard sequences Geometric or linear convergence: for some β (0 , 1) and q > 0 , and for all k e ( x k ) k . Superlinear convergence: for every

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Lect05 - D Bertsekas EE553 LECTURE 5 LECTURE OUTLINE...

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