Course Hero Logo
Question
Answered

i need details of these 2 math questions . these questions are...

i need details of these 2 math questions .

these questions are about optimization (basics of set-constrained and unconstrained optimization)


Image transcription text

6.12 Consider the problem minimize f (ac) subject to a: 6 Q, where f : R2 a R is given by f(:c) = 5:32 with a: = [$1,32]T, and Q = {a3 = [m1,z:2]T :xf +132 2 1}. a. Does the point :6" = [0, 1]T satisfy the first-order necessary condition? 1). Does the point (3" = [0, 1]T satisfy the second-order necessary condition? 0. Is the point 9;" = [0, 1]T a local minimizer?

... Show more

Image transcription text

6.32 Prove the following generalization of the second-order sufficient condi- tion: Theorem: Let Q be a. convex subset of IR", f E (32 a. real—valued function on Q, and m" a point in 9. Suppose that there exists a E R, c > 0, such that for all feasible directions or! at :3" (d 75 0), the following hold: 1. dTVf(a:*) 2 o. 2. dTF(a:*)d 2 clldllz. Then, cc" is a strict local minimizer of f.

... Show more

Answer & Explanation
Verified Solved by verified expert
Rated

cing elit. Nam lacinia pulvinar

ce dui lectus, congue vel laoreet ac, dictum vitae odio. Donec aliquet. Lorem ipsum dolor sit amet, consectetur adipiscing elit. Nam lacinia pulvinar tortor nec facilisis. Pellentesque dapibus efficitur laoreet. Nam risus ante, dapibus a molestie consequat, ultrices ac magna. Fusce dui lectu

Unlock full access to Course Hero

Explore over 16 million step-by-step answers from our library

Subscribe to view answer
1 Attachment
Answers4ad32.pdf
pdf
Recently Asked Questions
Explore recently asked questions from the same subject