Fdtxjr

Malcev's paper "On a class of homogeneous spaces" in English

How do I draw and define two right triangles next to each other?

Are the number of citations and number of published articles the most important criteria for a tenure promotion?

Meaning of に in 本当に

Why are electrically insulating heatsinks so rare? Is it just cost?

Theorems that impeded progress

How is it possible to have an ability score that is less than 3?

Character reincarnated...as a snail

Did Shadowfax go to Valinor?

What does "Puller Prush Person" mean?

Modeling an IP Address

How to format long polynomial?

What is a clear way to write a bar that has an extra beat?

Why is consensus so controversial in Britain?

Find the result of this dual key cipher

Which country benefited the most from UN Security Council vetoes?

tikz convert color string to hex value

Paid for article while in US on F-1 visa?

What defenses are there against being summoned by the Gate spell?

Is it legal for company to use my work email to pretend I still work there?

Can an x86 CPU running in real mode be considered to be basically an 8086 CPU?

Why do I get two different answers for this counting problem?

Can you really stack all of this on an Opportunity Attack?

Why is Minecraft giving an OpenGL error?

Norm of $|(x-x^*,y-y^*,z-z^*) |leq |nabla J(x,y,z)|$

$f(y) leq f(x)+nabla f(x)cdot (y-x) $ and $f(x)geq 0$ implies that $f$ is constant.minimizing a norm and a linear functionhessian matrix not positive definite at a minimum?Testing critical points using newton-raphson methodHessian-Matrix positive definite $iff$ $a$ local minimum?Is it possible to argue that $nabla F(x^*)neq textbf0$?Prove that if $nabla f(x_0) = 0$ and $nabla^2f(x_0) succeq0$ then $x_0$ couldn't be local minimum.Showing that for real $0<x_i, 0<q$ with $x_1…x_n=q^n$ it holds that $(1+x_1)…(1+x_n)geq(1+q)^n$Every local minimum of $f(x) = frac12x^tAx + b^tx +c$ is also a global minimumMinimize quadratic function with gradient descent method

0

$begingroup$

I want to prove that

$$|(x-x^*,y-y^*,z-z^*)|leq |nabla J(x,y,z)|,$$

where $J(x,y,z)=exp(fracx+y+z2016)+fracx^2+2y^2+3z^22$ and $(x^*,y^*,z^*)$ is the minimum of $J$.

Also, I have $$|(x-x^*,y-y^*,z-z^*) |^2leq U^t H U$$ with $H$ the Hessian matrix of $J$ and $$U=(x-x^*,y-y^*,z-z^*).$$

Could you give me some clue to complete the proof?

Thanks!

optimization

share|cite|improve this question

edited Mar 21 at 19:45

Bernard

124k741116

asked Mar 21 at 19:30

Alex PozoAlex Pozo

519214

$endgroup$

add a comment | 

0

$begingroup$

I want to prove that

$$|(x-x^*,y-y^*,z-z^*)|leq |nabla J(x,y,z)|,$$

where $J(x,y,z)=exp(fracx+y+z2016)+fracx^2+2y^2+3z^22$ and $(x^*,y^*,z^*)$ is the minimum of $J$.

Also, I have $$|(x-x^*,y-y^*,z-z^*) |^2leq U^t H U$$ with $H$ the Hessian matrix of $J$ and $$U=(x-x^*,y-y^*,z-z^*).$$

Could you give me some clue to complete the proof?

Thanks!

optimization

share|cite|improve this question

edited Mar 21 at 19:45

Bernard

124k741116

asked Mar 21 at 19:30

Alex PozoAlex Pozo

519214

$endgroup$

add a comment | 

$begingroup$

I want to prove that

$$|(x-x^*,y-y^*,z-z^*)|leq |nabla J(x,y,z)|,$$

where $J(x,y,z)=exp(fracx+y+z2016)+fracx^2+2y^2+3z^22$ and $(x^*,y^*,z^*)$ is the minimum of $J$.

Also, I have $$|(x-x^*,y-y^*,z-z^*) |^2leq U^t H U$$ with $H$ the Hessian matrix of $J$ and $$U=(x-x^*,y-y^*,z-z^*).$$

Could you give me some clue to complete the proof?

Thanks!

optimization

share|cite|improve this question

edited Mar 21 at 19:45

Bernard

124k741116

asked Mar 21 at 19:30

Alex PozoAlex Pozo

519214

$endgroup$

share|cite|improve this question

edited Mar 21 at 19:45

Bernard

124k741116

asked Mar 21 at 19:30

Alex PozoAlex Pozo

519214

share|cite|improve this question

edited Mar 21 at 19:45

Bernard

124k741116

asked Mar 21 at 19:30

Alex PozoAlex Pozo

519214

edited Mar 21 at 19:45

Bernard

124k741116

edited Mar 21 at 19:45

Bernard

124k741116

asked Mar 21 at 19:30

Alex PozoAlex Pozo

519214

asked Mar 21 at 19:30

Alex PozoAlex Pozo

519214