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1. Substitute z = 1-2-y in problem (1) to obtain an equivalent unconstrained optimization problem involving only variables 2 and y. 2. Starting at point (x, y) = (2,3), do one iteration of steepest descent. Is the result- ing point optimal? 3. Starting at point (x, y) = (2,3), do one iteration of Newton method. Is the result- ing point optimal?

1. Substitute z = 1-2-y in problem (1) to obtain an equivalent unconstrained optimization problem involving only variables 2 and y. 2. Starting at point (x, y) = (2,3), do one iteration of steepest descent. Is the result- ing point optimal? 3. Starting at point (x, y) = (2,3), do one iteration of Newton method. Is the result- ing point optimal?

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 17EQ
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We want to compute the projection of the point (x, y, z) = (2, 3, 5) into the plane x+y+ z = 1 (that is, find the closest point to (2,3,5) satisfying x+y+z=1). This projection can be found by solving the constrained optimization problem min (x - 2)² + (y - 3)² + (z − 5)² s.t. x+y+z=1 x, y, z € R. (1) (2) 1. Substitute z = 1 - x - y in problem (1) to obtain an equivalent unconstrained optimization problem involving only variables 2 and y. 2. Starting at point (x, y) = (2,3), do one iteration of steepest descent. Is the result- ing point optimal? 3. Starting at point (x, y) = (2,3), do one iteration of Newton method. Is the result- ing point optimal?
Transcribed Image Text:We want to compute the projection of the point (x, y, z) = (2, 3, 5) into the plane x+y+ z = 1 (that is, find the closest point to (2,3,5) satisfying x+y+z=1). This projection can be found by solving the constrained optimization problem min (x - 2)² + (y - 3)² + (z − 5)² s.t. x+y+z=1 x, y, z € R. (1) (2) 1. Substitute z = 1 - x - y in problem (1) to obtain an equivalent unconstrained optimization problem involving only variables 2 and y. 2. Starting at point (x, y) = (2,3), do one iteration of steepest descent. Is the result- ing point optimal? 3. Starting at point (x, y) = (2,3), do one iteration of Newton method. Is the result- ing point optimal?
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