# Tagged Questions

Optimization is the process of choosing the "best" value among possible values. They are often formulated as questions on the minimization/maximization of functions, with or without constraints.

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### How to prove the sum of squares is minimum?

Given $n$ positive values. Their sum is $k$. $$x_1 + x_2 + \cdots + x_n = k$$ The sum of their squares is defined as: $$x_1^2 + x_2^2 + \cdots + x_n^2$$ I think that the sum of squares is ...
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### Newton's method in higher dimensions explained

I'm studying about Newton's method and I get the single dimension case perfectly, but the multidimensional version makes me ask question... In Wikipedia Newton's method in higher dimensions is ...
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### How to interpret Hessian of a function

I know that gradient of a function gives the direction in which the directional derivative of the function is maximum. Is there any similar interpretation of Hessian ?
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### Applying the Lagrangian function to find critical points

So I have the following function $$f(x,y) = x^2+y^2$$ subject to $$g(x,y) = x+y-1 = 0.$$ And I have to use the Lagrangian to find the critical points, and determine wether they are ...
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### Trace minimization when some matrix is unknown

The problem is as follows: $\displaystyle\min_{V}$ trace($V^TH^T\Phi HV$)$\\$ s.t. $V^TV=I_d$ in the case when $H$ is not known. When $H$ is known, the solution is given by the eigenvectors ...