Compute the minimum-norm solution of the system

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Reference no: EM132302155

Math Optimization Problems -

Textbook - Numerical Optimization, Second Edition, by Jorge Nocedal and Stephen J. Wright. ISBN-10: 0-387-30303-0.

Problem 1 - Do Exercise 19.7: Program the simple interior-point method Algorithm 19.1 and apply it to the problem (18.69). Use the same starting point as in that problem. Try different values for the parameter σ.

Problem 2 - Do Exercise 19.8: (a) Compute the minimum-norm solution of the system of equations defined by (19.35). (This system defines the Newton component in the dogleg method used to find an approximate solution to (19.34).) Show that the computation of the Newton component can use the factorization of the augmented matrix defined in (19.36).

(b) Compute the unconstrained minimizer of the quadratic in (19.34a) along the steepest descent direction, starting from v 0. (This minimizer defines the Cauchy component in the dogleg method used to find an approximate solution to (19.34).)

(c) The dogleg step is a combination of the Newton and Cauchy steps from parts (a) and (b). Show that the dogleg step is in the range space of Aˆ^T.

Reference no: EM132302155

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