Mathematics Stack Exchange
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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.

2947 questions
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Overdetermined set of quadratic equations

I am having a set of equations of the form $$\begin{align} (x - a_1)^2 + (y - b_1)^2 + (z - c_1)^2 &= W_1\\ (x - a_2)^2 + (y - b_2)^2 + (z - c_2)^2 &= W_2\\ & \vdots \\ (x - a_m)^2 + (y - b_m)^2 + (z - c_m)^2 &= W_m. \end{align}$$ Here…
maths-help-seeker
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1 answer

Optimisation Problem

Given a vector $\vec{c}$ and a radius $r$, solve the problem: \begin{equation*} \begin{aligned} & \underset{x}{\text{maximise}} & & \vec{c} \cdotp \vec{x}=a \\ & \text{subject to} & & ||x^2||=r^2 \end{aligned} \end{equation*}
jp412
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