Mathematics Stack Exchange
Mathematics Stack Exchange

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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Optimization method

I have an optimization problem: [\begin{array}{l} \mathop {\max }\limits_{x,y} f(x,y)\\ 0 \le x \le g(y)\\ 0 \le y \le 1 \end{array}] f is non linear in x and y. f is increasing in x and decreasing in y. g(y) is increasing in y. Can we take x=g(y)…
wafa
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Optimization problem

I have a function $ f(x)= \vert x\vert ^3, x\in \Bbb{R^n} $ I have to compute the inverse of the Hessian by using the formula $(I+uu^T)^{-1} = I - {1\over 2}uu^T $, where $I$ is an identity $nxn$ matrix and and unit vector $u\in \Bbb{R^n} $. I have…
Pol
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Non Linear optimization of non central parameter

optimize for $p_{i}$, $i$ = 1,2,3. $(\frac{p_{3}}{1-p_3}(\mu_3 - \sum_{i=1}^{3}p_{i}\mu_i)^2)$ given that $\sum_{i=1}^{3}p_{i}\mu_{i}-\mu_3\leq 0$ and $\sum_{i=1}^{3}p_{i} = 1$. $0\leq p_i\leq 1$ for $i = 1,2,3.$ KKT may help
Satya Prakash
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How Can i Solve for K1, K2,..K6?

I'm working on Radial Distortion Correction: I'm having an Equation in the form: $$ r= r'((1+ K1.r'^2+ K2.r'^4+ K3.r'^6)/(1+ K4.r'^2+ K5.r'^4+ K6.r'^6)) $$ How can i solve for K1,K2,K3,K4,K5 & K6? Note: r,r' are known variables Std. Equation of…
Balaji R
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What exactly are convex constraints?

I haven't been able to find a clear answer to this question, seek an answer from a professor or figure it out myself as I am not a mathematics expert. I used the nonlinear-optimization but I'm not sure this is specific enough, so I invite you to add…
Ulf Aslak
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Solving a system of coupled nonlinear equations analytically rather than numerically

Let $x,y$ be two variables. Consider the following system: $$ \begin{cases} x=a_0+b (1+y^2/x^2)^{-1/2} \\ y=a_1+b(1+x^2/y^2)^{-1/2}, \end{cases}$$ where $a_0,a_1,b$ are parameters. I can solve this using numerical solvers, but it's very inefficient.…
yoki
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Is this illustration of Gauss Newton wrong?

In this illustration the value of each iteration is the minimum of the 2nd derivative. But the Wikipedia page says: the advantage [of the Gauss–Newton algorithm] is second derivatives, which can be challenging to compute, are not…
Vadi
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Finding the value of coefficients of a equation using non-linear least square method.

I have the following data: x: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 y: 22 36 42 51 57 64 68 71 75 79 85 87 88 91 94 97 99 99 103 104 105 107 108 109 111 I want to fit the data in the following equation…
J Cian
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Minimum of the sum of two functions

I want to show that trying to find the minimum of the sum of two or more functions of two different groups is a not convex problem. For example: $ \min\limits_{Y,Z} f(X,Y,Z)=...$. Moreover the values $X,Y,Z$ are matrices. My idea is to show that the…
N8_Coder
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invert S shape logistic curve fitting

I have a function F(x) = a + b / (1 + exp(-(cx + d))) and a small data set containing 5 sample: x = [10.0, 5.0, 2.0, 0.5, 0.25] and y = [23, 24, 25, 26, 27]. How can I find the suitable parameters, that is , a, b, c and d to fit this sample to the…
Li Yang
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Necessary Conditions for Saddle Value point

This questions is from the Kuhn-Tucker paper "Nonlinear Programming" in Section 2 Lemma 1. I don't understand how those conditions are necessary for a saddle point. I always thought that a saddle point was defined where the gradient is zero and the…
user178563
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Broyden's Method mismatched dimensions

Compute the first two iterates $\mathbf{x}^{(1)}$, $\mathbf{x}^{(2)}$ using Broyden's Method for the initial point $\mathbf{x}^{(0)}=(1,4)$ and the function $f(x_{1},x_{2})=3x_{1}^2+x_{2}^2-x_1x_2$ with $D_0=I$. Does this question even make sense?…
user3649110
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Solve: tanh(x) = a*x + b - most efficient way

I work on DSP code, where some equations are of form: tanh(x) = a*x + b (tanh or other hyperbolic functions) Currently I use Newton-Raphson method. Is there a better/faster method of finding solution for this case? I can use values in precomputed…
user1132968
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How to linearize this mixed-integer nonlinear constraint

Can someone please help me to linearize the following nonlinear/nonconvex constraint: $\sum\limits_{n=1}^Na_n\rm{log_2}(1+x_ny_n)\le M\delta$ Here $a_n \in\{0,1\}$, binary integer variable $0\le x_n \le 3$, continuous variable (bounded) $\delta$, a…
Dimitrios
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How to linearise this nonlinear constraint

I want to linearize or convexify this following constraint. Here $c_t$ is binary integer variables, $p_t$ are continuous variable which are bounded. $\gamma$ is a continuous variable. $h_t$ and $V$ are known…
Dimitrios
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