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Consider an optimization problem with no constraints. If a function f of n variables has a local maximum at z = (zi,2, ..., ) then select ALL that is TRUE. (You may select more than one) O Hessian matrix of f is positive definite at z Of(2,2,,) = 0 O(, ) < 0 Oz is a saddle point O 2 (1,,) = 0 O z is an exctreme value Oz is a stationary point O Hessian matrix of f is indefinite at z O (,2,zn) = 0 O Hessian matrix of f is negative definite at z' O A small movement in any direction away from z' results in a increase in the value of the function f. O(, ,) > 0 O A small movement in any direction away from z results in a decrease in the value of the function f.

Consider an optimization problem with no constraints. If a function f of n variables has a local maximum at z = (zi,2, ..., ) then select ALL that is TRUE. (You may select more than one) O Hessian matrix of f is positive definite at z Of(2,2,,) = 0 O(, ) < 0 Oz is a saddle point O 2 (1,,) = 0 O z is an exctreme value Oz is a stationary point O Hessian matrix of f is indefinite at z O (,2,zn) = 0 O Hessian matrix of f is negative definite at z' O A small movement in any direction away from z' results in a increase in the value of the function f. O(, ,) > 0 O A small movement in any direction away from z results in a decrease in the value of the function f.

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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(21,, Consider an optimization problem with no constraints. If a function f of n variables has a local maximum at T = TRUE. (You may select more than one) ..., then select ALL that is O Hessian matrix of f is positive definite at z OA(,,.,) < 0 Oz is a saddle point O f2 (,,., I) = 0 O z is an exctreme value Oz is a stationary point O Hessian matrix of f is indefinite at z O fn (,,.,I) =0 O Hessian matrix of f is negative definite at z O A small movement in any direction away from z results in a increase in the value of the function f. O fn (,, z,) > 0 O A small movement in any direction away from a results in a decrease in the value of the function f.
Transcribed Image Text:(21,, Consider an optimization problem with no constraints. If a function f of n variables has a local maximum at T = TRUE. (You may select more than one) ..., then select ALL that is O Hessian matrix of f is positive definite at z OA(,,.,) < 0 Oz is a saddle point O f2 (,,., I) = 0 O z is an exctreme value Oz is a stationary point O Hessian matrix of f is indefinite at z O fn (,,.,I) =0 O Hessian matrix of f is negative definite at z O A small movement in any direction away from z results in a increase in the value of the function f. O fn (,, z,) > 0 O A small movement in any direction away from a results in a decrease in the value of the function f.
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