# Tagged Questions

A non-linear optimization problem includes an objective function (to be minimized or maximized) and some number of equality and/or inequality constraints where the objective or some of the constraints are non-linear. Use this tag for questions related to the theory of solving such problems or for ...

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### nonlinear KKT analysis with bounded variables

By the help of lagrangian multipliers, I am solving a nonlinear problem with 6 variables using KKT analysis. At the beginning, I do not consider any upper-bound for the variables to see whether the ...
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### Nonlinear Multivariate Regression

Assuming I know exactly my forward model, which is represented by $n$ non-linear functions, or some probability models: $\vec{R}=f(x,y,z)$ , $f:\mathbb{R}^3\to\mathbb{R}^n$ Where each item in $R_i$ ...
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### Solving a nonlinear equation $\sum_{z=0}^{s} \frac{(\lambda(l-x))^z}{z!} e^{-\lambda(l-x)}=p$

I would appreciate it if someone helps me with solving the following equation. Suppose $\lambda,l \in R^+$, $p\in[0,1]$, and $s\in N_{0}$. How can we find an $x\in [0,l]$, which satisfies the ...
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### What is the easiest way to optimize the weighted sum of L2 norms?

I have the following cost function (solving for $M$ - the $x_i$s are known): minimize $\sum_i\sum_j(w_{ij} \cdot (x_i-x_j)^T\cdot M\cdot(x_i-x_j))$ ($w_{ij} \in [-1,1]$) subject to: $M \succeq 0$ (...
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### Does $\min\{x_1x_3+x_2^2 | x_1^2+x_2^2+x_3^4 = 4\}$ has an optimal solution?
Does $\min\{x_1x_3+x_2^2 | x_1^2+x_2^2+x_3^4 = 4\}$ has an optimal solution? I think continuous function over closed and bounded domain has an optimal solution but I am not sure. Can anyone give me ...
The title is general, but what I am specifically interested in, is how to solve the following problem: $$\text{Maximize } c$$ $$\text{Subject to:}$$ $$a+b+c<0$$ $$b^2-4ac<0$$ a,b \in \...