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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Suitable Loss function for Order preserving Factoring of a matrix?

(Old-Question) Given a $n\times n$ symmetric matrix $X$, I would like to factor it using a vector $c$ of size $n \times 1$ such that: $\sum_{i,j} [X_{ij} \cdot c_i\cdot c_j]$ is minimum. How can I ...
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find the area of the largest rectangle that can fit inside a semi circle of radius 2 cm

find the area of the largest rectangle that can fit inside a semi circle of radius 2 cm I have absolutely no idea where to get started on this...What I did do is $A=(\pi r^2)/2$ (its a semi circle) ...
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Optimization problem with two-step discontinuous function

imagine my function as a staircase with two steps. This function is to be fitted to some empirical data and I'm searching for an algorithm which minimizes the Root Mean Squared Error between this ...
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How do I guess an intital step length in a line search (minimization)?

I am currently trying to write a "simple" minimizer for a function $y = f(x)$ where $x$ is a multidimensional vector and $y$ is a real number where I have access to the derivate vector. If I have a ...
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Lp optimal solution question

i have a general question. if there is a general LP problem $c^Tx$ s.t $A\cdot x \le b$, and $x \ge 0$ and assuming that the components of $c$ are non-zero entries then how can I prove that when $x$ ...
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Minimum for this function

What is the minimum for this function of $x_1,x_2, \ldots, x_n$: $$\sum_{i=1}^n c_i \log x_i + \lambda \; \sum_{i=1}^n d_i x_i, $$ where $\lambda$, $c$ and $d$ series are positive constants, $x_i ...