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Questions tagged [nonlinear-optimization]

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 trying to solve particular problems.

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. Usually, non-linear optimization problems are much harder to solve than linear ones.

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with a set of arbitrary initial values in newton method the system of equations don't have any answer

with a set of arbitrary initial values in newton method the system of equations don't have any answer. Does it mean that this system of equation don't have any answer at all or may be there exists a set of initial values for which this set has…
soodeh
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Finding the maximum and minimum value a number can take in a set whose mean and rms is constrained

I'm a freshman in college with no prior experience in non linear optimization. This is a question I encountered in an MCQ format. Problem $\ x_i \epsilon Z $ $\ i = {1,2,3,4,5} $ $\sum_{i=1}^5 x_i = 10$ $\sum_{i=1}^5 x_i^2 = 40$ Find the maximum…
Glaxionaizer
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Quasiconvex objective function with nonlinear constraint

I have the following optimization problem: $$\min \frac{F}{A}+c_p D K \sqrt{A}+c_g \Theta^2+c_e a D + t e (1-\Theta) D+ \frac{t a}{A}$$ s.t. $a \leq [e (1-\Theta) D A] p_a$ $$\Theta \leq p_\Theta$$ $$\Theta, \quad A \geq 0, \quad A>0$$ Decision…
Larusso
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Constrained optimization problem of 4 variables!

I am stuck with this problem. I thought of trying to first solve the problem with weak inequalities for all the constraints using Kuhn Tucker conditions, and checking for solutions at which the constraints for $s$ and $t$ are slack. It is getting…
bitter-sweet
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Creating gradient functions based on model parameters?

I am using a software library (Math.Net) to try to fit two Lorentzians to a curve. I have found some example software which shows the fitting out a few various types of curves (Line, Parabola, Power Function, and a Sum of Trigonometric functions). I…
KDecker
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School District Boundary Optimization--Interpreting the Objective Function

I’m looking for a little help on a new problem. I’m in a linear programming class and trying to work on a project exploring methods on nonlinear optimization and I came across the following question in a book: Minimize the total distance traveled…
jadellos
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Question regarding Kuhn-Tucker multiplier

I have a problem which I am unable to solve. If we consider the following problem $\min f(x)$, $G(x) = b$; where $f$ is in $C^2(R^n)$, and $G$ from $R^n$ to $R^m$ is a $C^2$-function, $G = (g_1,\ldots , g_m)^t$ (transpose) , and $b \in R^m$. If…
nada
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What class of problem is a set of equations using inequalities and if-then-else?

Can you please identify what class of problem this is so that I can research algorithms for solving it please? Its a a set of linear equations and inequalities/constraints looking like this: a = 3*g b = 1*h + 2 c = 1 d = 2 e = if (a >= b) then 1…
daw
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Is there any "equivalence" to maximizing $\inf{f_i(y)}$?

I have to maximize the function $g(y) = inf_i{\|y - x_i\|_2}$ subject to $y\in B_0(1)\subset\mathbb{R}^n$. Then I thought that maybe there is an averaging or mollifying of the functions (using partition of unity of some sort) that might do the…
bernatguillen
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Is it possible to solve this 2D geolocation problem?

I have $N$ equations: $$R_i=\alpha_i\frac{T_i}{(x-x_i)^2+(y-y_i)^2}, i=1..N$$ $T_i>0$, $0 < \alpha_i < 1$ and so $R_i>0$. $R_i$, $x_i$ and $y_i$ are known quantities; $x$, $y$, $T_i$ and $\alpha_i$ are unknowns and so I have $2+2N$ unknowns. Is it…
Alessandro Jacopson
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Function Optimization

Assume any recursive function like: (just for example, my rekursive function is just too big to write) $x_{n+1}=\frac{(x_{n}-3)^{5}x_{n}^{2}}{a\sqrt{x_{n}}}$ (or any other non-linear function) Is there any optimization-algorithm, which allows me…
N8_Coder
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How to solve the fractional polynomial optimization problem?

The optimization problem has a fractional of polynomials as the objective function, with linear constraint. For example, $\min\limits_{x,y}\quad…
Bob
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Prove a specific Cartan matrix is positive definite

I am trying to prove that the following matrix is positive definite, but I am stuck in the last step of my proof... Any help would be really appreciated. Thanks! Question Let $A$ be a matrix with entries as follows: $$A_{ii}=2,…
s1047857
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understanding a statement in Gill, Murray and Wright "Practical Optimization"

Hi: I'm reading the book "Practical Optimization" and there's a part in Chapter 3 that I can't prove to myself but I'm sure it's true. On page 64, they define the Taylor expansion of $F$ about $x^{*}$: (3.3) $F(x^{*} + \epsilon p) = F(x^{*}) +…
mark leeds
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Non-linear optimization with unknown derivative and real numbers only

Background I'm trying to optimize a set of 7 parameters which are the core configuration of some external engine (specifically Solr parameters). I already have an optimization function which grades the results. The idea was to use Nelder Mead…
Eran H.
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