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Consider the problem minimize f(x1, x2) = (x2 – x†)(x2 – 2x}). - (i) Show that the first- and second-order necessary conditions for optimality are satisfied at (0, 0)". (ii) Show that the origin is a local minimizer of f along any line passing through the origin (that is, x2 = (iii) Show that the origin is not a local minimizer of f (consider, for example, curves of the form x2 = kx-). What conclusions can you draw from this? mx1).

Consider the problem minimize f(x1, x2) = (x2 – x†)(x2 – 2x}). - (i) Show that the first- and second-order necessary conditions for optimality are satisfied at (0, 0)". (ii) Show that the origin is a local minimizer of f along any line passing through the origin (that is, x2 = (iii) Show that the origin is not a local minimizer of f (consider, for example, curves of the form x2 = kx-). What conclusions can you draw from this? mx1).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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2.7. Consider the problem minimize f(x1, x2) = (x2 – x})(x2 – 2x}). (i) Show that the first- and second-order necessary conditions for optimality are satisfied at (0, 0)". (ii) Show that the origin is a local minimizer of f along any line passing through the origin (that is, x2 = mx1). (iii) Show that the origin is not a local minimizer of f (consider, for example, curves of the form x2 = kx-). What conclusions can you draw from this?
Transcribed Image Text:2.7. Consider the problem minimize f(x1, x2) = (x2 – x})(x2 – 2x}). (i) Show that the first- and second-order necessary conditions for optimality are satisfied at (0, 0)". (ii) Show that the origin is a local minimizer of f along any line passing through the origin (that is, x2 = mx1). (iii) Show that the origin is not a local minimizer of f (consider, for example, curves of the form x2 = kx-). What conclusions can you draw from this?
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